feat: add stats/base/dists/planck/cdf

PR-URL: #4130
Co-authored-by: Athan Reines <kgryte@gmail.com>
Reviewed-by: Athan Reines <kgryte@gmail.com>

lib/node_modules/@stdlib/stats/base/dists/planck/cdf/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2024 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.
+
+-->
+
+# Cumulative Distribution Function
+
+> Planck (discrete exponential) distribution [cumulative distribution function][cdf].
+
+<section class="intro">
+
+The [cumulative distribution function][cdf] for a Planck random variable is
+
+<!-- <equation class="equation" label="eq:planck_cdf" align="center" raw="F(x;\lambda) = 1 - e^{-\lambda \cdot (\lfloor x \rfloor + 1)}" alt="CDF for a Planck distribution."> -->
+
+```math
+F(x;\lambda) = 1 - e^{-\lambda (\lfloor x \rfloor + 1)}
+```
+
+<!-- </equation> -->
+
+where `λ` is the shape parameter and `x` denotes the count of events in a quantized system.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var cdf = require( '@stdlib/stats/base/dists/planck/cdf' );
+```
+
+#### cdf( x, lambda )
+
+Evaluates the [cumulative distribution function][cdf] for a Planck (discrete exponential) distribution with shape parameter `lambda`.
+
+```javascript
+var y = cdf( 2.0, 0.5 );
+// returns ~0.7769
+
+y = cdf( 2.0, 1.5 );
+// returns ~0.9889
+```
+
+If provided `NaN` as any argument, the function returns `NaN`.
+
+```javascript
+var y = cdf( NaN, 0.5 );
+// returns NaN
+
+y = cdf( 0.0, NaN );
+// returns NaN
+```
+
+If provided a shape parameter `lambda` which is nonpositive, the function returns `NaN`.
+
+```javascript
+var y = cdf( 2.0, -1.0 );
+// returns NaN
+```
+
+#### cdf.factory( lambda )
+
+Returns a function for evaluating the [cumulative distribution function][cdf] of a Planck (discrete exponential) distribution with shape parameter `lambda`.
+
+```javascript
+var mycdf = cdf.factory( 1.5 );
+var y = mycdf( 3.0 );
+// returns ~0.9975
+
+y = mycdf( 1.0 );
+// returns ~0.9502
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var cdf = require( '@stdlib/stats/base/dists/planck/cdf' );
+
+var x = discreteUniform( 10, 0, 5 );
+var lambda = uniform( 10, 0.1, 5.0 );
+
+var y;
+var i;
+for ( i = 0; i < lambda.length; i++ ) {
+    y = cdf( x[ i ], lambda[ i ] );
+    console.log( 'x: %d, λ: %d, F(x;λ): %d', x[ i ].toFixed( 4 ), lambda[ i ].toFixed( 4 ), y.toFixed( 4 ) );
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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">
+
+[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/dists/planck/cdf/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var cdf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var lambda;
+	var x;
+	var y;
+	var i;
+
+	x = discreteUniform( 100, 0, 40 );
+	lambda = uniform( 100, 0.1, 10.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = cdf( x[ i % x.length ], lambda[ i % lambda.length ] );
+		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();
+});
+
+bench( pkg+':factory', function benchmark( b ) {
+	var mycdf;
+	var x;
+	var y;
+	var i;
+
+	x = discreteUniform( 100, 0, 40 );
+	mycdf = cdf.factory( 0.3 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		y = mycdf( x[ i % x.length ] );
+		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();
+});

lib/node_modules/@stdlib/stats/base/dists/planck/cdf/docs/repl.txt

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+
+{{alias}}( x, λ )
+    Evaluates the cumulative distribution function (CDF) for a Planck
+    distribution with shape parameter `λ` at a value `x`.
+
+    If provided `NaN` as any argument, the function returns `NaN`.
+
+    If `λ <= 0`, the function returns `NaN`.
+
+    Parameters
+    ----------
+    x: number
+        Input value.
+
+    λ: number
+        Shape parameter.
+
+    Returns
+    -------
+    out: number
+        Evaluated CDF.
+
+    Examples
+    --------
+    > var y = {{alias}}( 2.0, 0.5 )
+    ~0.7769
+    > y = {{alias}}( 2.0, 1.5 )
+    ~0.9889
+    > y = {{alias}}( -1.0, 4.0 )
+    0.0
+    > y = {{alias}}( NaN, 0.5 )
+    NaN
+    > y = {{alias}}( 0.0, NaN )
+    NaN
+    // Invalid shape parameter
+    > y = {{alias}}( 2.0, -1.4 )
+    NaN
+
+
+{{alias}}.factory( λ )
+    Returns a function for evaluating the cumulative distribution function (CDF)
+    of a Planck distribution with shape parameter `λ`.
+
+    Parameters
+    ----------
+    λ: number
+        Shape parameter.
+
+    Returns
+    -------
+    cdf: Function
+        Cumulative distribution function (CDF).
+
+    Examples
+    --------
+    > var mycdf = {{alias}}.factory( 1.5 );
+    > var y = mycdf( 3.0 )
+    ~0.9975
+    > y = mycdf( 1.0 )
+    ~0.9502
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/stats/base/dists/planck/cdf/docs/types/index.d.ts

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+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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
+
+/**
+* Evaluates the cumulative distribution function (CDF) for a Planck distribution.
+*
+* @param x - input value
+* @returns evaluated CDF
+*/
+type Unary = ( x: number ) => number;
+
+/**
+* Interface for the cumulative distribution function (CDF) of a Planck distribution.
+*/
+interface CDF {
+	/**
+	* Evaluates the cumulative distribution function (CDF) for a Planck distribution with shape parameter `lambda` at a value `x`.
+	*
+	* ## Notes
+	*
+	* -   If `lambda <= 0`, the function returns `NaN`.
+	*
+	* @param x - input value
+	* @param lambda - shape parameter
+	* @returns evaluated CDF
+	*
+	* @example
+	* var y = cdf( 2.0, 0.5 );
+	* // returns ~0.7769
+	*
+	* @example
+	* var y = cdf( 2.0, 1.5 );
+	* // returns ~0.9889
+	*
+	* @example
+	* var y = cdf( -1.0, 0.5 );
+	* // returns 0.0
+	*
+	* @example
+	* var y = cdf( NaN, 0.5 );
+	* // returns NaN
+	*
+	* @example
+	* var y = cdf( 0.0, NaN );
+	* // returns NaN
+	*
+	* @example
+	* // Invalid probability
+	* var y = cdf( 2.0, 1.4 );
+	* // returns NaN
+	*/
+	( x: number, lambda: number ): number;
+
+	/**
+	* Returns a function for evaluating the cumulative distribution function (CDF) for a Planck distribution with shape parameter `lambda`.
+	*
+	* @param lambda - shape parameter
+	* @returns CDF
+	*
+	* @example
+	* var mycdf = cdf.factory( 1.5 );
+	* var y = mycdf( 3.0 );
+	* // returns ~0.9975
+	*
+	* y = mycdf( 1.0 );
+	* // returns ~0.9502
+	*/
+	factory( lambda: number ): Unary;
+}
+
+/**
+* Planck distribution cumulative distribution function (CDF).
+*
+* @param x - input value
+* @param lambda - shape parameter
+* @returns evaluated CDF
+*
+* @example
+* var y = cdf( 2.0, 0.5 );
+* // returns ~0.7769
+*
+* y = cdf( 2.0, 1.5 );
+* // returns ~0.9889
+*
+* var mycdf = cdf.factory( 1.5 );
+* y = mycdf( 3.0 );
+* // returns ~0.9975
+*
+* y = mycdf( 1.0 );
+* // returns ~0.9502
+*/
+declare var cdf: CDF;
+
+
+// EXPORTS //
+
+export = cdf;