From ab976504c211b7d6208a7413e2d1ed4e0d31d325 Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Fri, 9 Jan 2026 01:35:49 +0530
Subject: [PATCH 01/10] feat: add variance implementation for half-normal
 distribution

---
 .../base/dists/halfnormal/variance/README.md  | 244 ++++++++++++++++++
 .../variance/benchmark/benchmark.js           |  52 ++++
 .../variance/benchmark/benchmark.native.js    |  67 +++++
 .../halfnormal/variance/benchmark/c/Makefile  | 146 +++++++++++
 .../variance/benchmark/c/benchmark.c          | 138 ++++++++++
 .../dists/halfnormal/variance/binding.gyp     | 170 ++++++++++++
 .../dists/halfnormal/variance/docs/repl.txt   |  33 +++
 .../halfnormal/variance/docs/types/index.d.ts |  52 ++++
 .../halfnormal/variance/docs/types/test.ts    |  42 +++
 .../halfnormal/variance/examples/c/Makefile   | 146 +++++++++++
 .../halfnormal/variance/examples/c/example.c  |  38 +++
 .../halfnormal/variance/examples/index.js     |  39 +++
 .../dists/halfnormal/variance/include.gypi    |  53 ++++
 .../stats/base/dists/halfnormal/variance.h    |  38 +++
 .../dists/halfnormal/variance/lib/index.js    |  43 +++
 .../dists/halfnormal/variance/lib/main.js     |  64 +++++
 .../dists/halfnormal/variance/lib/native.js   |  58 +++++
 .../dists/halfnormal/variance/manifest.json   |  79 ++++++
 .../dists/halfnormal/variance/package.json    |  66 +++++
 .../dists/halfnormal/variance/src/Makefile    |  70 +++++
 .../dists/halfnormal/variance/src/addon.c     |  23 ++
 .../base/dists/halfnormal/variance/src/main.c |  38 +++
 .../variance/test/fixtures/julia/REQUIRE      |   3 +
 .../variance/test/fixtures/julia/data.json    |   1 +
 .../variance/test/fixtures/julia/runner.jl    |  57 ++++
 .../dists/halfnormal/variance/test/test.js    |  90 +++++++
 .../halfnormal/variance/test/test.native.js   |  94 +++++++
 27 files changed, 1944 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.native.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/c/Makefile
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/c/benchmark.c
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/binding.gyp
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/repl.txt
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/types/index.d.ts
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/types/test.ts
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/Makefile
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/example.c
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/include.gypi
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/include/stdlib/stats/base/dists/halfnormal/variance.h
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/index.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/main.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/native.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/manifest.json
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/package.json
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/Makefile
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/addon.c
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/main.c
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/REQUIRE
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/data.json
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/runner.jl
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
new file mode 100644
index 000000000000..2d7e7f303729
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
@@ -0,0 +1,244 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# Variance
+
+> [Half-normal][half-normal-distribution] distribution [variance][variance].
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+The [variance][variance] for a [half-normal][half-normal-distribution] random variable with scale parameter `σ > 0` is
+
+<!-- <equation class="equation" label="eq:halfnormal_variance" align="center" raw="\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)" alt="Variance for a half-normal distribution."> -->
+
+```math
+\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)" data-equation="eq:halfnormal_variance">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/img/equation_halfnormal_variance.svg" alt="Variance for a half-normal distribution.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var variance = require( '@stdlib/stats/base/dists/halfnormal/variance' );
+```
+
+#### variance( sigma )
+
+Returns the [variance][variance] for a [half-normal][half-normal-distribution] distribution with scale parameter `sigma`.
+
+```javascript
+var y = variance( 1.0 );
+// returns ~0.363
+
+y = variance( 4.0 );
+// returns ~5.818
+
+y = variance( 0.5 );
+// returns ~0.091
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = variance( NaN );
+// returns NaN
+```
+
+If provided `sigma <= 0`, the function returns `NaN`.
+
+```javascript
+var y = variance( 0.0 );
+// returns NaN
+
+y = variance( -1.0 );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var variance = require( '@stdlib/stats/base/dists/halfnormal/variance' );
+
+var opts = {
+    'dtype': 'float64'
+};
+var sigma = uniform( 10, 0.0, 20.0, opts );
+
+logEachMap( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, variance );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for C API documentation. -->
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C API usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/stats/base/dists/halfnormal/variance.h"
+```
+
+#### stdlib_base_dists_halfnormal_variance( sigma )
+
+Returns the variance for a [half-normal][half-normal-distribution] distribution with scale parameter `sigma`.
+
+-   **sigma**: `[in] double` scale parameter.
+-   **return**: `[out] double` variance.
+
+```c
+double stdlib_base_dists_halfnormal_variance( const double sigma );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/stats/base/dists/halfnormal/variance.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+static double random_uniform( const double min, const double max ) {
+    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+    return min + ( v*(max-min) );
+}
+
+int main( void ) {
+    double sigma;
+    double y;
+    int i;
+
+    for ( i = 0; i < 10; i++ ) {
+        sigma = random_uniform( 0.1, 20.0 );
+        y = stdlib_base_dists_halfnormal_variance( sigma );
+        printf( "σ: %.4f, Var(X;σ): %.4f\n", sigma, y );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[half-normal-distribution]: https://en.wikipedia.org/wiki/Half-normal_distribution
+
+[variance]: https://en.wikipedia.org/wiki/Variance
+
+
+<!-- /.links -->
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.js
new file mode 100644
index 000000000000..4a91c801e414
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.js
@@ -0,0 +1,52 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var randu = require( '@stdlib/random/base/randu' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+var variance = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var sigma;
+	var y;
+	var i;
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		sigma = ( randu()*20.0 ) + EPS;
+		y = variance( sigma );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.native.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.native.js
new file mode 100644
index 000000000000..68fd3c78f660
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.native.js
@@ -0,0 +1,67 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var Float64Array = require( '@stdlib/array/float64' );
+var uniform = require( '@stdlib/random/base/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var variance = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( variance instanceof Error )
+};
+
+
+// MAIN //
+
+bench( pkg+'::native', opts, function benchmark( b ) {
+	var sigma;
+	var len;
+	var y;
+	var i;
+
+	len = 100;
+	sigma = new Float64Array( len );
+	for ( i = 0; i < len; i++ ) {
+		sigma[ i ] = uniform( EPS, 20.0 );
+	}
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = variance( sigma[ i % len ] );
+		if ( isnan( y ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( y ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/c/Makefile b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/c/Makefile
new file mode 100644
index 000000000000..979768abbcec
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/c/Makefile
@@ -0,0 +1,146 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2026 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+	QUIET := @
+else
+	QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+	OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+	CC := $(C_COMPILER)
+else
+	CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+	-std=c99 \
+	-O3 \
+	-Wall \
+	-pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+	fPIC ?=
+else
+	fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := benchmark.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+	$(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled benchmarks.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+	$(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+	$(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/c/benchmark.c b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/c/benchmark.c
new file mode 100644
index 000000000000..d36b7906a4c8
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/c/benchmark.c
@@ -0,0 +1,138 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#include "stdlib/stats/base/dists/halfnormal/variance.h"
+#include <stdlib.h>
+#include <stdio.h>
+#include <math.h>
+#include <time.h>
+#include <sys/time.h>
+
+#define NAME "halfnormal-variance"
+#define ITERATIONS 1000000
+#define REPEATS 3
+
+/**
+* Prints the TAP version.
+*/
+static void print_version( void ) {
+	printf( "TAP version 13\n" );
+}
+
+/**
+* Prints the TAP summary.
+*
+* @param total     total number of tests
+* @param passing   total number of passing tests
+*/
+static void print_summary( int total, int passing ) {
+	printf( "#\n" );
+	printf( "1..%d\n", total ); // TAP plan
+	printf( "# total %d\n", total );
+	printf( "# pass  %d\n", passing );
+	printf( "#\n" );
+	printf( "# ok\n" );
+}
+
+/**
+* Prints benchmarks results.
+*
+* @param elapsed   elapsed time in seconds
+*/
+static void print_results( double elapsed ) {
+	double rate = (double)ITERATIONS / elapsed;
+	printf( "  ---\n" );
+	printf( "  iterations: %d\n", ITERATIONS );
+	printf( "  elapsed: %0.9f\n", elapsed );
+	printf( "  rate: %0.9f\n", rate );
+	printf( "  ...\n" );
+}
+
+/**
+* Returns a clock time.
+*
+* @return clock time
+*/
+static double tic( void ) {
+	struct timeval now;
+	gettimeofday( &now, NULL );
+	return (double)now.tv_sec + (double)now.tv_usec/1.0e6;
+}
+
+/**
+* Generates a random number on the interval [min,max).
+*
+* @param min    minimum value (inclusive)
+* @param max    maximum value (exclusive)
+* @return       random number
+*/
+static double random_uniform( const double min, const double max ) {
+	double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+	return min + ( v*(max-min) );
+}
+
+/**
+* Runs a benchmark.
+*
+* @return elapsed time in seconds
+*/
+static double benchmark( void ) {
+	double elapsed;
+	double sigma[ 100 ];
+	double y;
+	double t;
+	int i;
+
+	for ( i = 0; i < 100; i++ ) {
+		sigma[ i ] = random_uniform( 0.1, 10.0 );
+	}
+
+	t = tic();
+	for ( i = 0; i < ITERATIONS; i++ ) {
+		y = stdlib_base_dists_halfnormal_variance( sigma[ i%100 ] );
+		if ( y != y ) {
+			printf( "should not return NaN\n" );
+			break;
+		}
+	}
+	elapsed = tic() - t;
+	if ( y != y ) {
+		printf( "should not return NaN\n" );
+	}
+	return elapsed;
+}
+
+/**
+* Main execution sequence.
+*/
+int main( void ) {
+	double elapsed;
+	int i;
+
+	// Use the current time to seed the random number generator:
+	srand( time( NULL ) );
+
+	print_version();
+	for ( i = 0; i < REPEATS; i++ ) {
+		printf( "# c::%s\n", NAME );
+		elapsed = benchmark();
+		print_results( elapsed );
+		printf( "ok %d benchmark finished\n", i+1 );
+	}
+	print_summary( REPEATS, REPEATS );
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/binding.gyp b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/binding.gyp
new file mode 100644
index 000000000000..0d6508a12e99
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/binding.gyp
@@ -0,0 +1,170 @@
+# @license Apache-2.0
+#
+# Copyright (c) 2026 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# A `.gyp` file for building a Node.js native add-on.
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+  # List of files to include in this file:
+  'includes': [
+    './include.gypi',
+  ],
+
+  # Define variables to be used throughout the configuration for all targets:
+  'variables': {
+    # Target name should match the add-on export name:
+    'addon_target_name%': 'addon',
+
+    # Set variables based on the host OS:
+    'conditions': [
+      [
+        'OS=="win"',
+        {
+          # Define the object file suffix:
+          'obj': 'obj',
+        },
+        {
+          # Define the object file suffix:
+          'obj': 'o',
+        }
+      ], # end condition (OS=="win")
+    ], # end conditions
+  }, # end variables
+
+  # Define compile targets:
+  'targets': [
+
+    # Target to generate an add-on:
+    {
+      # The target name should match the add-on export name:
+      'target_name': '<(addon_target_name)',
+
+      # Define dependencies:
+      'dependencies': [],
+
+      # Define directories which contain relevant include headers:
+      'include_dirs': [
+        # Local include directory:
+        '<@(include_dirs)',
+      ],
+
+      # List of source files:
+      'sources': [
+        '<@(src_files)',
+      ],
+
+      # Settings which should be applied when a target's object files are used as linker input:
+      'link_settings': {
+        # Define libraries:
+        'libraries': [
+          '<@(libraries)',
+        ],
+
+        # Define library directories:
+        'library_dirs': [
+          '<@(library_dirs)',
+        ],
+      },
+
+      # C/C++ compiler flags:
+      'cflags': [
+        # Enable commonly used warning options:
+        '-Wall',
+
+        # Aggressive optimization:
+        '-O3',
+      ],
+
+      # C specific compiler flags:
+      'cflags_c': [
+        # Specify the C standard to which a program is expected to conform:
+        '-std=c99',
+      ],
+
+      # C++ specific compiler flags:
+      'cflags_cpp': [
+        # Specify the C++ standard to which a program is expected to conform:
+        '-std=c++11',
+      ],
+
+      # Linker flags:
+      'ldflags': [],
+
+      # Apply conditions based on the host OS:
+      'conditions': [
+        [
+          'OS=="mac"',
+          {
+            # Linker flags:
+            'ldflags': [
+              '-undefined dynamic_lookup',
+              '-Wl,-no-pie',
+              '-Wl,-search_paths_first',
+            ],
+          },
+        ], # end condition (OS=="mac")
+        [
+          'OS!="win"',
+          {
+            # C/C++ flags:
+            'cflags': [
+              # Generate platform-independent code:
+              '-fPIC',
+            ],
+          },
+        ], # end condition (OS!="win")
+      ], # end conditions
+    }, # end target <(addon_target_name)
+
+    # Target to copy a generated add-on to a standard location:
+    {
+      'target_name': 'copy_addon',
+
+      # Declare that the output of this target is not linked:
+      'type': 'none',
+
+      # Define dependencies:
+      'dependencies': [
+        # Require that the add-on be generated before building this target:
+        '<(addon_target_name)',
+      ],
+
+      # Define a list of actions:
+      'actions': [
+        {
+          'action_name': 'copy_addon',
+          'message': 'Copying addon...',
+
+          # Explicitly list the inputs in the command-line invocation below:
+          'inputs': [],
+
+          # Declare the expected outputs:
+          'outputs': [
+            '<(addon_output_dir)/<(addon_target_name).node',
+          ],
+
+          # Define the command-line invocation:
+          'action': [
+            'cp',
+            '<(PRODUCT_DIR)/<(addon_target_name).node',
+            '<(addon_output_dir)/<(addon_target_name).node',
+          ],
+        },
+      ], # end actions
+    }, # end target copy_addon
+  ], # end targets
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/repl.txt
new file mode 100644
index 000000000000..5e31c5605fd3
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/repl.txt
@@ -0,0 +1,33 @@
+
+{{alias}}( σ )
+    Returns the variance of a half-normal distribution with scale
+    parameter `σ`.
+
+    If provided `NaN` as any argument, the function returns `NaN`.
+
+    If provided `σ <= 0`, the function returns `NaN`.
+
+    Parameters
+    ----------
+    σ: number
+        Scale parameter.
+
+    Returns
+    -------
+    out: number
+        Variance.
+
+    Examples
+    --------
+    > var y = {{alias}}( 1.0 )
+    ~0.3633802276
+    > y = {{alias}}( 5.0 )
+    ~9.0845056908
+    > y = {{alias}}( NaN )
+    NaN
+    > y = {{alias}}( 0.0 )
+    NaN
+
+    See Also
+    --------
+
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/types/index.d.ts
new file mode 100644
index 000000000000..43aa994c78a2
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/types/index.d.ts
@@ -0,0 +1,52 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// TypeScript Version: 4.1
+
+/**
+* Returns the variance for a half-normal distribution with scale parameter `sigma`.
+*
+* ## Notes
+*
+* -   If provided `sigma <= 0`, the function returns `NaN`.
+*
+* @param sigma - scale parameter
+* @returns variance
+*
+* @example
+* var y = variance( 1.0 );
+* // returns ~0.3633802276
+*
+* @example
+* var y = variance( 5.0 );
+* // returns ~9.0845056908
+*
+* @example
+* var y = variance( NaN );
+* // returns NaN
+*
+* @example
+* var y = variance( 0.0 );
+* // returns NaN
+*/
+declare function variance( sigma: number ): number;
+
+
+// EXPORTS //
+
+export = variance;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/types/test.ts
new file mode 100644
index 000000000000..bd3d947eae4f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/docs/types/test.ts
@@ -0,0 +1,42 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+import variance = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	variance( 2 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a value other than a number...
+{
+	variance( true ); // $ExpectError
+	variance( false ); // $ExpectError
+	variance( '5' ); // $ExpectError
+	variance( [] ); // $ExpectError
+	variance( {} ); // $ExpectError
+	variance( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided insufficient arguments...
+{
+	variance(); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/Makefile b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/Makefile
new file mode 100644
index 000000000000..c8f8e9a1517b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/Makefile
@@ -0,0 +1,146 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2026 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+	QUIET := @
+else
+	QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+	OS := WINNT
+endif
+endif
+endif
+endif
+
+# Define the program used for compiling C source files:
+ifdef C_COMPILER
+	CC := $(C_COMPILER)
+else
+	CC := gcc
+endif
+
+# Define the command-line options when compiling C files:
+CFLAGS ?= \
+	-std=c99 \
+	-O3 \
+	-Wall \
+	-pedantic
+
+# Determine whether to generate position independent code ([1][1], [2][2]).
+#
+# [1]: https://gcc.gnu.org/onlinedocs/gcc/Code-Gen-Options.html#Code-Gen-Options
+# [2]: http://stackoverflow.com/questions/5311515/gcc-fpic-option
+ifeq ($(OS), WINNT)
+	fPIC ?=
+else
+	fPIC ?= -fPIC
+endif
+
+# List of includes (e.g., `-I /foo/bar -I /beep/boop/include`):
+INCLUDE ?=
+
+# List of source files:
+SOURCE_FILES ?=
+
+# List of libraries (e.g., `-lopenblas -lpthread`):
+LIBRARIES ?=
+
+# List of library paths (e.g., `-L /foo/bar -L /beep/boop`):
+LIBPATH ?=
+
+# List of C targets:
+c_targets := example.out
+
+
+# RULES #
+
+#/
+# Compiles source files.
+#
+# @param {string} [C_COMPILER] - C compiler (e.g., `gcc`)
+# @param {string} [CFLAGS] - C compiler options
+# @param {(string|void)} [fPIC] - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} [INCLUDE] - list of includes (e.g., `-I /foo/bar -I /beep/boop/include`)
+# @param {string} [SOURCE_FILES] - list of source files
+# @param {string} [LIBPATH] - list of library paths (e.g., `-L /foo/bar -L /beep/boop`)
+# @param {string} [LIBRARIES] - list of libraries (e.g., `-lopenblas -lpthread`)
+#
+# @example
+# make
+#
+# @example
+# make all
+#/
+all: $(c_targets)
+
+.PHONY: all
+
+#/
+# Compiles C source files.
+#
+# @private
+# @param {string} CC - C compiler (e.g., `gcc`)
+# @param {string} CFLAGS - C compiler options
+# @param {(string|void)} fPIC - compiler flag determining whether to generate position independent code (e.g., `-fPIC`)
+# @param {string} INCLUDE - list of includes (e.g., `-I /foo/bar`)
+# @param {string} SOURCE_FILES - list of source files
+# @param {string} LIBPATH - list of library paths (e.g., `-L /foo/bar`)
+# @param {string} LIBRARIES - list of libraries (e.g., `-lopenblas`)
+#/
+$(c_targets): %.out: %.c
+	$(QUIET) $(CC) $(CFLAGS) $(fPIC) $(INCLUDE) -o $@ $(SOURCE_FILES) $< $(LIBPATH) -lm $(LIBRARIES)
+
+#/
+# Runs compiled examples.
+#
+# @example
+# make run
+#/
+run: $(c_targets)
+	$(QUIET) ./$<
+
+.PHONY: run
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean:
+	$(QUIET) -rm -f *.o *.out
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/example.c b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/example.c
new file mode 100644
index 000000000000..bbc51f993865
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/example.c
@@ -0,0 +1,38 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#include "stdlib/stats/base/dists/halfnormal/variance.h"
+#include <stdlib.h>
+#include <stdio.h>
+
+static double random_uniform( const double min, const double max ) {
+	double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
+	return min + ( v*(max-min) );
+}
+
+int main( void ) {
+	double sigma;
+	double y;
+	int i;
+
+	for ( i = 0; i < 10; i++ ) {
+		sigma = random_uniform( 0.0, 20.0 );
+		y = stdlib_base_dists_halfnormal_variance( sigma );
+		printf( "σ: %.4f, Var(X;σ): %.4f\n", sigma, y );
+	}
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
new file mode 100644
index 000000000000..52bda6676058
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
@@ -0,0 +1,39 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEach = require( '@stdlib/console/log-each' );
+var Float64Array = require( '@stdlib/array/float64' );
+var variance = require( './../lib' );
+
+var opts = {
+	'dtype': 'float64'
+};
+
+// Generate positive standard deviations:
+var sigma = uniform( 10, 0.1, 20.0, opts );
+var v = new Float64Array( sigma.length );
+
+var i;
+for ( i = 0; i < sigma.length; i++ ) {
+	v[ i ] = variance( sigma[ i ] );
+}
+
+logEach( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, v );
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/include.gypi b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/include.gypi
new file mode 100644
index 000000000000..bee8d41a2caf
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/include.gypi
@@ -0,0 +1,53 @@
+# @license Apache-2.0
+#
+# Copyright (c) 2026 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+# A GYP include file for building a Node.js native add-on.
+#
+# Main documentation:
+#
+# [1]: https://gyp.gsrc.io/docs/InputFormatReference.md
+# [2]: https://gyp.gsrc.io/docs/UserDocumentation.md
+{
+  # Define variables to be used throughout the configuration for all targets:
+  'variables': {
+    # Source directory:
+    'src_dir': './src',
+
+    # Include directories:
+    'include_dirs': [
+      '<!@(node -e "var arr = require(\'@stdlib/utils/library-manifest\')(\'./manifest.json\',{},{\'basedir\':process.cwd(),\'paths\':\'posix\'}).include; for ( var i = 0; i < arr.length; i++ ) { console.log( arr[ i ] ); }")',
+    ],
+
+    # Add-on destination directory:
+    'addon_output_dir': './src',
+
+    # Source files:
+    'src_files': [
+      '<(src_dir)/addon.c',
+      '<!@(node -e "var arr = require(\'@stdlib/utils/library-manifest\')(\'./manifest.json\',{},{\'basedir\':process.cwd(),\'paths\':\'posix\'}).src; for ( var i = 0; i < arr.length; i++ ) { console.log( arr[ i ] ); }")',
+    ],
+
+    # Library dependencies:
+    'libraries': [
+      '<!@(node -e "var arr = require(\'@stdlib/utils/library-manifest\')(\'./manifest.json\',{},{\'basedir\':process.cwd(),\'paths\':\'posix\'}).libraries; for ( var i = 0; i < arr.length; i++ ) { console.log( arr[ i ] ); }")',
+    ],
+
+    # Library directories:
+    'library_dirs': [
+      '<!@(node -e "var arr = require(\'@stdlib/utils/library-manifest\')(\'./manifest.json\',{},{\'basedir\':process.cwd(),\'paths\':\'posix\'}).libpath; for ( var i = 0; i < arr.length; i++ ) { console.log( arr[ i ] ); }")',
+    ],
+  }, # end variables
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/include/stdlib/stats/base/dists/halfnormal/variance.h b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/include/stdlib/stats/base/dists/halfnormal/variance.h
new file mode 100644
index 000000000000..aa8e8eeebe16
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/include/stdlib/stats/base/dists/halfnormal/variance.h
@@ -0,0 +1,38 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#ifndef STDLIB_STATS_BASE_DISTS_HALFNORMAL_VARIANCE_H
+#define STDLIB_STATS_BASE_DISTS_HALFNORMAL_VARIANCE_H
+
+/*
+* If C++, prevent name mangling so that the compiler emits a binary file having undecorated names, thus mirroring the behavior of a C compiler.
+*/
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+* Returns the variance for a half-normal distribution with scale parameter `sigma`.
+*/
+double stdlib_base_dists_halfnormal_variance( const double sigma );
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif // !STDLIB_STATS_BASE_DISTS_HALFNORMAL_VARIANCE_H
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/index.js
new file mode 100644
index 000000000000..904e5daa0d90
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/index.js
@@ -0,0 +1,43 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+/**
+* Half-normal distribution variance.
+*
+* @module @stdlib/stats/base/dists/halfnormal/variance
+*
+* @example
+* var variance = require( '@stdlib/stats/base/dists/halfnormal/variance' );
+*
+* var y = variance( 1.0 );
+* // returns ~0.3633802276324186
+*
+* y = variance( 4.0 );
+* // returns ~5.814083642118698
+*/
+
+// MODULES //
+
+var variance = require( '@stdlib/stats/base/dists/halfnormal/variance/lib/main.js' );
+
+
+// EXPORTS //
+
+module.exports = variance;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/main.js
new file mode 100644
index 000000000000..3c30bcfd8d1c
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/main.js
@@ -0,0 +1,64 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var PI = require( '@stdlib/constants/float64/pi' );
+
+
+// MAIN //
+
+/**
+* Returns the variance for a half-normal distribution with scale parameter `sigma`.
+*
+* @param {PositiveNumber} sigma - scale parameter
+* @returns {number} variance
+*
+* @example
+* var y = variance( 1.0 );
+* // returns ~0.3633802276324186
+*
+* @example
+* var y = variance( 4.0 );
+* // returns ~5.814083642118698
+*
+* @example
+* var y = variance( NaN );
+* // returns NaN
+*
+* @example
+* var y = variance( 0.0 );
+* // returns NaN
+*/
+function variance( sigma ) {
+	if (
+		isnan( sigma ) ||
+		sigma <= 0.0
+	) {
+		return NaN;
+	}
+	return ( sigma * sigma ) * ( 1.0 - ( 2.0 / PI ) );
+}
+
+
+// EXPORTS //
+
+module.exports = variance;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/native.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/native.js
new file mode 100644
index 000000000000..7fb20459e18c
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/native.js
@@ -0,0 +1,58 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var addon = require( './../src/addon.node' );
+
+
+// MAIN //
+
+/**
+* Returns the variance for a half-normal distribution with scale parameter `sigma`.
+*
+* @private
+* @param {PositiveNumber} sigma - scale parameter
+* @returns {number} variance
+*
+* @example
+* var y = variance( 1.0 );
+* // returns ~0.3633802276324186
+*
+* @example
+* var y = variance( 4.0 );
+* // returns ~5.814083642118698
+*
+* @example
+* var y = variance( NaN );
+* // returns NaN
+*
+* @example
+* var y = variance( 0.0 );
+* // returns NaN
+*/
+function variance( sigma ) {
+	return addon( sigma );
+}
+
+
+// EXPORTS //
+
+module.exports = variance;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/manifest.json
new file mode 100644
index 000000000000..66a545f26bfd
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/manifest.json
@@ -0,0 +1,79 @@
+{
+  "options": {
+    "task": "build",
+    "wasm": false
+  },
+  "fields": [
+    {
+      "field": "src",
+      "resolve": true,
+      "relative": true
+    },
+    {
+      "field": "include",
+      "resolve": true,
+      "relative": true
+    },
+    {
+      "field": "libraries",
+      "resolve": false,
+      "relative": false
+    },
+    {
+      "field": "libpath",
+      "resolve": true,
+      "relative": false
+    }
+  ],
+  "confs": [
+    {
+      "task": "build",
+      "wasm": false,
+      "src": [
+        "./src/main.c"
+      ],
+      "include": [
+        "./include"
+      ],
+      "libraries": [],
+      "libpath": [],
+      "dependencies": [
+        "@stdlib/math/base/napi/unary",
+        "@stdlib/math/base/assert/is-nan",
+        "@stdlib/constants/float64/pi"
+      ]
+    },
+    {
+      "task": "benchmark",
+      "wasm": false,
+      "src": [
+        "./src/main.c"
+      ],
+      "include": [
+        "./include"
+      ],
+      "libraries": [],
+      "libpath": [],
+      "dependencies": [
+        "@stdlib/math/base/assert/is-nan",
+        "@stdlib/constants/float64/pi"
+      ]
+    },
+    {
+      "task": "examples",
+      "wasm": false,
+      "src": [
+        "./src/main.c"
+      ],
+      "include": [
+        "./include"
+      ],
+      "libraries": [],
+      "libpath": [],
+      "dependencies": [
+        "@stdlib/math/base/assert/is-nan",
+        "@stdlib/constants/float64/pi"
+      ]
+    }
+  ]
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/package.json b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/package.json
new file mode 100644
index 000000000000..3a343833f093
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/package.json
@@ -0,0 +1,66 @@
+{
+  "name": "@stdlib/stats/base/dists/halfnormal/variance",
+  "version": "0.0.0",
+  "description": "Half-normal distribution variance.",
+  "license": "Apache-2.0",
+  "author": {
+    "name": "The Stdlib Authors",
+    "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+  },
+  "contributors": [
+    {
+      "name": "The Stdlib Authors",
+      "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+    }
+  ],
+  "main": "./lib",
+  "gypfile": true,
+  "directories": {
+    "benchmark": "./benchmark",
+    "doc": "./docs",
+    "example": "./examples",
+    "include": "./include",
+    "lib": "./lib",
+    "src": "./src",
+    "test": "./test"
+  },
+  "types": "./docs/types",
+  "scripts": {},
+  "homepage": "https://github.com/stdlib-js/stdlib",
+  "repository": {
+    "type": "git",
+    "url": "git://github.com/stdlib-js/stdlib.git"
+  },
+  "bugs": {
+    "url": "https://github.com/stdlib-js/stdlib/issues"
+  },
+  "dependencies": {},
+  "devDependencies": {},
+  "engines": {
+    "node": ">=0.10.0",
+    "npm": ">2.7.0"
+  },
+  "os": [
+    "aix",
+    "darwin",
+    "freebsd",
+    "linux",
+    "macos",
+    "openbsd",
+    "sunos",
+    "win32",
+    "windows"
+  ],
+  "keywords": [
+    "stdlib",
+    "stdmath",
+    "statistics",
+    "stats",
+    "distribution",
+    "dist",
+    "parameter",
+    "continuous",
+    "halfnormal",
+    "univariate"
+  ]
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/Makefile b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/Makefile
new file mode 100644
index 000000000000..2caf905cedbe
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/Makefile
@@ -0,0 +1,70 @@
+#/
+# @license Apache-2.0
+#
+# Copyright (c) 2026 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#/
+
+# VARIABLES #
+
+ifndef VERBOSE
+	QUIET := @
+else
+	QUIET :=
+endif
+
+# Determine the OS ([1][1], [2][2]).
+#
+# [1]: https://en.wikipedia.org/wiki/Uname#Examples
+# [2]: http://stackoverflow.com/a/27776822/2225624
+OS ?= $(shell uname)
+ifneq (, $(findstring MINGW,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring MSYS,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring CYGWIN,$(OS)))
+	OS := WINNT
+else
+ifneq (, $(findstring Windows_NT,$(OS)))
+	OS := WINNT
+endif
+endif
+endif
+endif
+
+
+# RULES #
+
+#/
+# Removes generated files for building an add-on.
+#
+# @example
+# make clean-addon
+#/
+clean-addon:
+	$(QUIET) -rm -f *.o *.node
+
+.PHONY: clean-addon
+
+#/
+# Removes generated files.
+#
+# @example
+# make clean
+#/
+clean: clean-addon
+
+.PHONY: clean
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/addon.c b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/addon.c
new file mode 100644
index 000000000000..9ec7c0184b16
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/addon.c
@@ -0,0 +1,23 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#include "stdlib/stats/base/dists/halfnormal/variance.h"
+#include "stdlib/math/base/napi/unary.h"
+
+// cppcheck-suppress shadowFunction
+STDLIB_MATH_BASE_NAPI_MODULE_D_D( stdlib_base_dists_halfnormal_variance );
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/main.c
new file mode 100644
index 000000000000..57efe491909d
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/src/main.c
@@ -0,0 +1,38 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+#include "stdlib/stats/base/dists/halfnormal/variance.h"
+#include "stdlib/math/base/assert/is_nan.h"
+#include "stdlib/constants/float64/pi.h"
+
+/**
+* Returns the variance for a half-normal distribution with scale parameter `sigma`.
+*
+* @param sigma  scale parameter
+* @return       variance
+*
+* @example
+* double y = stdlib_base_dists_halfnormal_variance( 1.0 );
+* // returns ~0.3633802276
+*/
+double stdlib_base_dists_halfnormal_variance( const double sigma ) {
+	if ( stdlib_base_is_nan( sigma ) || sigma <= 0.0 ) {
+		return 0.0 / 0.0; // NaN
+	}
+	return ( sigma * sigma ) * ( 1.0 - ( 2.0 / STDLIB_CONSTANT_FLOAT64_PI ) );
+}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/REQUIRE
new file mode 100644
index 000000000000..98be20b58ed3
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/REQUIRE
@@ -0,0 +1,3 @@
+Distributions 0.23.8
+julia 1.5
+JSON 0.21
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/data.json
new file mode 100644
index 000000000000..e92f982df512
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/data.json
@@ -0,0 +1 @@
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diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/runner.jl
new file mode 100644
index 000000000000..85cf0a6327f8
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/fixtures/julia/runner.jl
@@ -0,0 +1,57 @@
+#!/usr/bin/env julia
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2026 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import JSON
+
+"""
+	gen( sigma, name )
+
+Generate fixture data for the variance of a half-normal distribution
+and write to file.
+
+# Arguments
+
+* `sigma::AbstractVector{<:Real}`: scale parameter (σ > 0)
+* `name::AbstractString`: output filename
+"""
+function gen( sigma, name )
+	c = 1.0 - ( 2.0 / π )
+
+	expected = Array{Float64}( undef, length( sigma ) )
+	for i in eachindex( sigma )
+		if sigma[ i ] > 0.0
+			expected[ i ] = ( sigma[ i ]^2 ) * c
+		else
+			expected[ i ] = NaN
+		end
+	end
+
+	data = Dict(
+		"sigma" => sigma,
+		"expected" => expected
+	)
+
+	open( name, "w" ) do io
+		write( io, JSON.json( data ) )
+		write( io, "\n" )
+	end
+end
+
+# Generate fixtures:
+sigma = rand( 1000 ) .* 5.0
+gen( sigma, "data.json" )
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.js
new file mode 100644
index 000000000000..8b98bf49f70c
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.js
@@ -0,0 +1,90 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+var variance = require( './../lib' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof variance, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'if provided `NaN` for `sigma`, the function returns `NaN`', function test( t ) {
+	var v = variance( NaN );
+	t.strictEqual( isnan( v ), true, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if provided a value less than or equal to 0 for `sigma`, the function returns `NaN`', function test( t ) {
+	var v;
+
+	v = variance( 0.0 );
+	t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+	v = variance( -1.0 );
+	t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+	v = variance( NINF );
+	t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function returns the variance of a half-normal distribution', function test( t ) {
+	var expected;
+	var delta;
+	var sigma;
+	var tol;
+	var v;
+	var i;
+
+	sigma = data.sigma;
+	expected = data.expected;
+
+	for ( i = 0; i < sigma.length; i++ ) {
+		v = variance( sigma[ i ] );
+		delta = abs( v - expected[ i ] );
+		tol = 1.0 * EPS * abs( expected[ i ] );
+
+		if ( expected[ i ] !== null ) {
+			if ( v === expected[ i ] || delta <= tol ) {
+				t.strictEqual( v, expected[ i ], 'sigma: '+sigma[ i ] );
+			} else {
+				t.ok( delta <= tol, 'within tolerance. σ: '+sigma[ i ] );
+			}
+		}
+	}
+	t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
new file mode 100644
index 000000000000..e7f32903b989
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
@@ -0,0 +1,94 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var resolve = require( 'path' ).resolve;
+var tape = require( 'tape' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
+
+
+// FIXTURES //
+
+var data = require( './fixtures/julia/data.json' );
+
+
+// VARIABLES //
+
+var variance = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( variance instanceof Error )
+};
+
+// TESTS //
+
+tape( 'main export is a function', opts, function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof variance, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'if provided `NaN`, the function returns `NaN`', opts, function test( t ) {
+	var y = variance( NaN );
+	t.strictEqual( isnan( y ), true, 'returns NaN' );
+	t.end();
+});
+
+tape( 'if provided a nonpositive `sigma`, the function returns `NaN`', opts, function test( t ) {
+	var y;
+
+	y = variance( 0.0 );
+	t.strictEqual( isnan( y ), true, 'returns NaN' );
+
+	y = variance( -1.0 );
+	t.strictEqual( isnan( y ), true, 'returns NaN' );
+
+	t.end();
+});
+
+tape( 'the function returns the variance of a half-normal distribution', opts, function test( t ) {
+	var expected;
+	var delta;
+	var sigma;
+	var tol;
+	var y;
+	var i;
+
+	expected = data.expected;
+	sigma = data.sigma;
+
+	for ( i = 0; i < sigma.length; i++ ) {
+		y = variance( sigma[ i ] );
+		delta = abs( y - expected[ i ] );
+		tol = 1.0 * EPS * abs( expected[ i ] );
+
+		if ( expected[ i ] !== null ) {
+			if ( y === expected[ i ] || delta <= tol ) {
+				t.strictEqual( y, expected[ i ], 'sigma: '+sigma[ i ] );
+			} else {
+				t.ok( delta <= tol, 'within tolerance. σ: '+sigma[ i ] );
+			}
+		}
+	}
+	t.end();
+});

From eac7a6bc01ad0bf550f69a6ab8b585f891d9d38d Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Fri, 9 Jan 2026 01:52:10 +0530
Subject: [PATCH 02/10] fix: add missing section in README

---
 .../@stdlib/stats/base/dists/halfnormal/variance/README.md     | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
index 2d7e7f303729..a72c9df4ea9f 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
@@ -64,7 +64,7 @@ var y = variance( 1.0 );
 // returns ~0.363
 
 y = variance( 4.0 );
-// returns ~5.818
+// returns ~5.814083642118698
 
 y = variance( 0.5 );
 // returns ~0.091
@@ -240,5 +240,6 @@ int main( void ) {
 
 [variance]: https://en.wikipedia.org/wiki/Variance
 
+</section>
 
 <!-- /.links -->

From 96d19ad1f4370ac02839385ff4705cc0b3324bc9 Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Fri, 9 Jan 2026 02:00:12 +0530
Subject: [PATCH 03/10] fix: add relative path to import

---
 .../@stdlib/stats/base/dists/halfnormal/variance/lib/index.js   | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/index.js
index 904e5daa0d90..0f32370a5a56 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/index.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/lib/index.js
@@ -35,7 +35,7 @@
 
 // MODULES //
 
-var variance = require( '@stdlib/stats/base/dists/halfnormal/variance/lib/main.js' );
+var variance = require( './main.js' );
 
 
 // EXPORTS //

From 68c6188fe9b23b148219ab3c0ff4ecfdf24f0d86 Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Fri, 9 Jan 2026 02:04:33 +0530
Subject: [PATCH 04/10] fix: additional space before header

---
 .../stats/base/dists/halfnormal/variance/test/test.native.js     | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
index e7f32903b989..654d600d12ad 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
@@ -40,6 +40,7 @@ var opts = {
 	'skip': ( variance instanceof Error )
 };
 
+
 // TESTS //
 
 tape( 'main export is a function', opts, function test( t ) {

From 6f33913f21c0748813c02da9678ae6951f89cbbb Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Sun, 11 Jan 2026 13:08:09 +0530
Subject: [PATCH 05/10] fix: add requested suggestions

---
 .../halfnormal/variance/examples/c/example.c      |  2 +-
 .../dists/halfnormal/variance/examples/index.js   | 15 +++------------
 .../base/dists/halfnormal/variance/package.json   |  3 +++
 .../base/dists/halfnormal/variance/test/test.js   | 10 +++++-----
 .../dists/halfnormal/variance/test/test.native.js | 12 ++++++++----
 5 files changed, 20 insertions(+), 22 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/example.c b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/example.c
index bbc51f993865..a040b9a8c8de 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/example.c
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/c/example.c
@@ -33,6 +33,6 @@ int main( void ) {
 	for ( i = 0; i < 10; i++ ) {
 		sigma = random_uniform( 0.0, 20.0 );
 		y = stdlib_base_dists_halfnormal_variance( sigma );
-		printf( "σ: %.4f, Var(X;σ): %.4f\n", sigma, y );
+		printf( "σ: %lf, Var(X;σ): %lf\n", sigma, y );
 	}
 }
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
index 52bda6676058..15966e31d489 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
@@ -19,21 +19,12 @@
 'use strict';
 
 var uniform = require( '@stdlib/random/array/uniform' );
-var logEach = require( '@stdlib/console/log-each' );
-var Float64Array = require( '@stdlib/array/float64' );
+var logEachMap = require( '@stdlib/console/log-each' );
 var variance = require( './../lib' );
 
 var opts = {
 	'dtype': 'float64'
 };
+var sigma = uniform( 10, 0.0, 20.0, opts );
 
-// Generate positive standard deviations:
-var sigma = uniform( 10, 0.1, 20.0, opts );
-var v = new Float64Array( sigma.length );
-
-var i;
-for ( i = 0; i < sigma.length; i++ ) {
-	v[ i ] = variance( sigma[ i ] );
-}
-
-logEach( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, v );
+logEachMap( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, variance );
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/package.json b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/package.json
index 3a343833f093..850c60878b20 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/package.json
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/package.json
@@ -60,6 +60,9 @@
     "dist",
     "parameter",
     "continuous",
+    "variance",
+    "spread",
+    "dispersion",
     "halfnormal",
     "univariate"
   ]
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.js
index 8b98bf49f70c..65fecaed2366 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.js
@@ -75,14 +75,14 @@ tape( 'the function returns the variance of a half-normal distribution', functio
 
 	for ( i = 0; i < sigma.length; i++ ) {
 		v = variance( sigma[ i ] );
-		delta = abs( v - expected[ i ] );
-		tol = 1.0 * EPS * abs( expected[ i ] );
 
 		if ( expected[ i ] !== null ) {
-			if ( v === expected[ i ] || delta <= tol ) {
-				t.strictEqual( v, expected[ i ], 'sigma: '+sigma[ i ] );
+			if ( v === expected[ i ] ) {
+				t.strictEqual( v, expected[i], ', sigma: '+sigma[i]+', v: '+v+', expected: '+expected[i] );
 			} else {
-				t.ok( delta <= tol, 'within tolerance. σ: '+sigma[ i ] );
+				delta = abs( v - expected[ i ] );
+				tol = 1.0 * EPS * abs( expected[ i ] );
+				t.ok( delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. v: '+v+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
 			}
 		}
 	}
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
index 654d600d12ad..bd81558662cf 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
@@ -25,6 +25,7 @@ var tape = require( 'tape' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var abs = require( '@stdlib/math/base/special/abs' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
 var EPS = require( '@stdlib/constants/float64/eps' );
 
 
@@ -64,8 +65,11 @@ tape( 'if provided a nonpositive `sigma`, the function returns `NaN`', opts, fun
 	y = variance( -1.0 );
 	t.strictEqual( isnan( y ), true, 'returns NaN' );
 
+	y = variance( NINF );
+	t.strictEqual( isnan( y ), true, 'returns expected value' );
+
 	t.end();
-});
+});	
 
 tape( 'the function returns the variance of a half-normal distribution', opts, function test( t ) {
 	var expected;
@@ -84,10 +88,10 @@ tape( 'the function returns the variance of a half-normal distribution', opts, f
 		tol = 1.0 * EPS * abs( expected[ i ] );
 
 		if ( expected[ i ] !== null ) {
-			if ( y === expected[ i ] || delta <= tol ) {
-				t.strictEqual( y, expected[ i ], 'sigma: '+sigma[ i ] );
+			if ( y === expected[ i ] ) {
+				t.strictEqual( y, expected[i], ', sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] );
 			} else {
-				t.ok( delta <= tol, 'within tolerance. σ: '+sigma[ i ] );
+				t.ok( delta <= tol, 'within tolerance. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
 			}
 		}
 	}

From f6b0f01074112f38feae3ec3e9dc2d8f66f36711 Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Sun, 11 Jan 2026 13:10:52 +0530
Subject: [PATCH 06/10] correction of import

---
 .../stats/base/dists/halfnormal/variance/examples/index.js      | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
index 15966e31d489..bb2f2a276cf7 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
@@ -19,7 +19,7 @@
 'use strict';
 
 var uniform = require( '@stdlib/random/array/uniform' );
-var logEachMap = require( '@stdlib/console/log-each' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
 var variance = require( './../lib' );
 
 var opts = {

From 2678965244956383d5714d6d419344d679b013f0 Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Sun, 11 Jan 2026 13:25:28 +0530
Subject: [PATCH 07/10] remove trailing space

---
 .../stats/base/dists/halfnormal/variance/test/test.native.js    | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
index bd81558662cf..26ee1b8910fe 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
@@ -69,7 +69,7 @@ tape( 'if provided a nonpositive `sigma`, the function returns `NaN`', opts, fun
 	t.strictEqual( isnan( y ), true, 'returns expected value' );
 
 	t.end();
-});	
+});
 
 tape( 'the function returns the variance of a half-normal distribution', opts, function test( t ) {
 	var expected;

From 55ca3e4469587d978112114a9689c017f588d8bd Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Mon, 12 Jan 2026 13:31:52 +0530
Subject: [PATCH 08/10] match exisiting template for variance docs

---
 .../base/dists/halfnormal/variance/README.md     | 16 ++++++++++++----
 .../halfnormal/variance/benchmark/benchmark.js   | 11 +++++++++--
 2 files changed, 21 insertions(+), 6 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
index a72c9df4ea9f..1ac0e020ec62 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
@@ -31,7 +31,7 @@ The [variance][variance] for a [half-normal][half-normal-distribution] random va
 <!-- <equation class="equation" label="eq:halfnormal_variance" align="center" raw="\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)" alt="Variance for a half-normal distribution."> -->
 
 ```math
-\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)
+\mathop{\mathrm{Var}}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)
 ```
 
 <!-- <div class="equation" align="center" data-raw-text="\operatorname{Var}\left[ X \right] = \sigma^{2} \left(1 - \frac{2}{\pi}\right)" data-equation="eq:halfnormal_variance">
@@ -61,7 +61,7 @@ Returns the [variance][variance] for a [half-normal][half-normal-distribution] d
 
 ```javascript
 var y = variance( 1.0 );
-// returns ~0.363
+// returns ~0.3633802276
 
 y = variance( 4.0 );
 // returns ~5.814083642118698
@@ -117,7 +117,7 @@ var opts = {
 };
 var sigma = uniform( 10, 0.0, 20.0, opts );
 
-logEachMap( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, variance );
+logEachMap( 'σ: %lf, Var(X;σ): %lf', sigma, variance );
 ```
 
 </section>
@@ -142,6 +142,8 @@ logEachMap( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, variance );
 
 <!-- Section for C API documentation. -->
 
+* * *
+
 <section class="c">
 
 ## C APIs
@@ -168,6 +170,12 @@ logEachMap( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, variance );
 
 Returns the variance for a [half-normal][half-normal-distribution] distribution with scale parameter `sigma`.
 
+```c
+double out = stdlib_base_dists_halfnormal_variance( 1.0 );
+// returns ~0.3633802276
+```
+The function accepts the following arguments:
+
 -   **sigma**: `[in] double` scale parameter.
 -   **return**: `[out] double` variance.
 
@@ -211,7 +219,7 @@ int main( void ) {
     for ( i = 0; i < 10; i++ ) {
         sigma = random_uniform( 0.1, 20.0 );
         y = stdlib_base_dists_halfnormal_variance( sigma );
-        printf( "σ: %.4f, Var(X;σ): %.4f\n", sigma, y );
+        printf( "σ: %lf, Var(X;σ): %lf\n", sigma, y );
     }
 }
 ```
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.js
index 4a91c801e414..71ce596970a1 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/benchmark/benchmark.js
@@ -21,6 +21,7 @@
 // MODULES //
 
 var bench = require( '@stdlib/bench' );
+var Float64Array = require( '@stdlib/array/float64' );
 var randu = require( '@stdlib/random/base/randu' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var EPS = require( '@stdlib/constants/float64/eps' );
@@ -32,13 +33,19 @@ var variance = require( './../lib' );
 
 bench( pkg, function benchmark( b ) {
 	var sigma;
+	var len;
 	var y;
 	var i;
 
+	len = 100;
+	sigma = new Float64Array( len );
+	for ( i = 0; i < len; i++ ) {
+		sigma[ i ] = ( randu() * 20.0 ) + EPS;
+	}
+
 	b.tic();
 	for ( i = 0; i < b.iterations; i++ ) {
-		sigma = ( randu()*20.0 ) + EPS;
-		y = variance( sigma );
+		y = variance( sigma[ i % len ] );
 		if ( isnan( y ) ) {
 			b.fail( 'should not return NaN' );
 		}

From 5532193d325b90f676912660f2eda8584cc8e6de Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Mon, 12 Jan 2026 16:02:15 +0530
Subject: [PATCH 09/10] update index.js

---
 .../@stdlib/stats/base/dists/halfnormal/variance/README.md      | 1 +
 .../stats/base/dists/halfnormal/variance/examples/index.js      | 2 +-
 2 files changed, 2 insertions(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
index 1ac0e020ec62..652754241455 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
@@ -174,6 +174,7 @@ Returns the variance for a [half-normal][half-normal-distribution] distribution
 double out = stdlib_base_dists_halfnormal_variance( 1.0 );
 // returns ~0.3633802276
 ```
+
 The function accepts the following arguments:
 
 -   **sigma**: `[in] double` scale parameter.
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
index bb2f2a276cf7..9687b4f4ecfe 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/examples/index.js
@@ -27,4 +27,4 @@ var opts = {
 };
 var sigma = uniform( 10, 0.0, 20.0, opts );
 
-logEachMap( 'σ: %0.4f, Var(X;σ): %0.4f', sigma, variance );
+logEachMap( 'σ: %lf, Var(X;σ): %lf', sigma, variance );

From e3378cbea21e0d57b60e7bb0c713288e6ffa2c6d Mon Sep 17 00:00:00 2001
From: Shubham <b4mshubham@gmail.com>
Date: Tue, 13 Jan 2026 11:03:16 +0530
Subject: [PATCH 10/10] add requested suggestions

---
 .../@stdlib/stats/base/dists/halfnormal/variance/README.md  | 1 -
 .../base/dists/halfnormal/variance/test/test.native.js      | 6 +++---
 2 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
index 652754241455..193696b7ef56 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/README.md
@@ -178,7 +178,6 @@ double out = stdlib_base_dists_halfnormal_variance( 1.0 );
 The function accepts the following arguments:
 
 -   **sigma**: `[in] double` scale parameter.
--   **return**: `[out] double` variance.
 
 ```c
 double stdlib_base_dists_halfnormal_variance( const double sigma );
diff --git a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
index 26ee1b8910fe..395e7a82e0a1 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/halfnormal/variance/test/test.native.js
@@ -52,7 +52,7 @@ tape( 'main export is a function', opts, function test( t ) {
 
 tape( 'if provided `NaN`, the function returns `NaN`', opts, function test( t ) {
 	var y = variance( NaN );
-	t.strictEqual( isnan( y ), true, 'returns NaN' );
+	t.strictEqual( isnan( y ), true, 'returns expected value' );
 	t.end();
 });
 
@@ -60,10 +60,10 @@ tape( 'if provided a nonpositive `sigma`, the function returns `NaN`', opts, fun
 	var y;
 
 	y = variance( 0.0 );
-	t.strictEqual( isnan( y ), true, 'returns NaN' );
+	t.strictEqual( isnan( y ), true, 'returns expected value' );
 
 	y = variance( -1.0 );
-	t.strictEqual( isnan( y ), true, 'returns NaN' );
+	t.strictEqual( isnan( y ), true, 'returns expected value' );
 
 	y = variance( NINF );
 	t.strictEqual( isnan( y ), true, 'returns expected value' );