Features:

- Realized Minima R^1 Rate Distribution (2, 3) Bug Fixes/Re-organization: - Two IID Sum Quadrature #1 (25, 26, 27) - Two IID Sum Quadrature #2 (28, 29, 30) - Two IID Sum Quadrature #3 (31, 32, 33) - Two IID Sum Quadrature #4 (34, 35, 36) - Two IID Sum Quadrature #5 (37, 38, 39) - Two IID Sum Quadrature #6 (40, 41, 42) Samples: - R^1 Minimum Rate Distribution #1 (1) - R^1 Minimum Rate Distribution #2 (4, 5, 6) - R^1 Minimum Rate Distribution #3 (7, 8, 9) - R^1 Minimum Rate Distribution #4 (10, 11, 12) - R^1 Minimum Rate Distribution #5 (13, 14, 15) - R^1 Two IID Significant Statistics #1 (16, 17, 18) - R^1 Two IID Significant Statistics #2 (19, 20, 21) - R^1 Two IID Significant Statistics #3 (22, 23, 24) - R^1 Two IID Significant Statistics #4 (43, 44, 45) - R^1 Two IID Significant Statistics #5 (46, 47, 48) - R^1 Two IID Significant Statistics #6 (49, 50, 51) - R^1 Two IID Significant Statistics #7 (52, 53, 54) - R^1 Two IID Significant Statistics #8 (55, 56, 57) - R^1 Two IID Significant Statistics #9 (58, 59, 60) IdeaDRIP:
lakshmiDRIP · Aug 14, 2023 · 6b264e0 · 6b264e0
1 parent e605b39
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diff --git a/ReleaseNotes/12_26_2022.txt b/ReleaseNotes/12_26_2022.txt
@@ -0,0 +1,35 @@
+
+Features:
+
+ - Realized Minima R^1 Rate Distribution (2, 3)
+
+
+Bug Fixes/Re-organization:
+
+ - Two IID Sum Quadrature #1 (25, 26, 27)
+ - Two IID Sum Quadrature #2 (28, 29, 30)
+ - Two IID Sum Quadrature #3 (31, 32, 33)
+ - Two IID Sum Quadrature #4 (34, 35, 36)
+ - Two IID Sum Quadrature #5 (37, 38, 39)
+ - Two IID Sum Quadrature #6 (40, 41, 42)
+
+
+Samples:
+
+ - R^1 Minimum Rate Distribution #1 (1)
+ - R^1 Minimum Rate Distribution #2 (4, 5, 6)
+ - R^1 Minimum Rate Distribution #3 (7, 8, 9)
+ - R^1 Minimum Rate Distribution #4 (10, 11, 12)
+ - R^1 Minimum Rate Distribution #5 (13, 14, 15)
+ - R^1 Two IID Significant Statistics #1 (16, 17, 18)
+ - R^1 Two IID Significant Statistics #2 (19, 20, 21)
+ - R^1 Two IID Significant Statistics #3 (22, 23, 24)
+ - R^1 Two IID Significant Statistics #4 (43, 44, 45)
+ - R^1 Two IID Significant Statistics #5 (46, 47, 48)
+ - R^1 Two IID Significant Statistics #6 (49, 50, 51)
+ - R^1 Two IID Significant Statistics #7 (52, 53, 54)
+ - R^1 Two IID Significant Statistics #8 (55, 56, 57)
+ - R^1 Two IID Significant Statistics #9 (58, 59, 60)
+
+
+IdeaDRIP:
diff --git a/src/main/java/org/drip/measure/exponential/RealizedMinimaR1RateDistribution.java b/src/main/java/org/drip/measure/exponential/RealizedMinimaR1RateDistribution.java
@@ -120,21 +120,21 @@ public class RealizedMinimaR1RateDistribution
  /**
  * Standard Instance of RealizedMinimaR1RateDistribution
  * 
- * @param r1RateDistributionArray R<sup>1</sup> Exponential Distribution Array
+ * @param lambdaArray Array of the Distribution Lambdas
  * 
  * @return Standard Instance of RealizedMinimaR1RateDistribution
  */
 
  public static final RealizedMinimaR1RateDistribution Standard (
- final R1RateDistribution[] r1RateDistributionArray)
+ final double[] lambdaArray)
  {
- if (null == r1RateDistributionArray)
+ if (null == lambdaArray)
  {
  return null;
  }
 
  double compositeDistributionLambda = 0.;
- int exponentialDistributionCount = r1RateDistributionArray.length;
+ int exponentialDistributionCount = lambdaArray.length;
 
  if (0 == exponentialDistributionCount)
  {
@@ -143,11 +143,17 @@ public static final RealizedMinimaR1RateDistribution Standard (
 
  try
  {
+ R1RateDistribution[] r1RateDistributionArray =
+ new R1RateDistribution[exponentialDistributionCount];
+
  for (int distributionIndex = 0;
  distributionIndex < exponentialDistributionCount;
  ++distributionIndex)
  {
- compositeDistributionLambda += r1RateDistributionArray[distributionIndex].rate();
+ r1RateDistributionArray[distributionIndex] =
+ new R1RateDistribution (lambdaArray[distributionIndex]);
+
+ compositeDistributionLambda += lambdaArray[distributionIndex];
  }
 
  return new RealizedMinimaR1RateDistribution (

diff --git a/src/main/java/org/drip/measure/exponential/TwoIIDSum.java b/src/main/java/org/drip/measure/exponential/TwoIIDSum.java
@@ -199,6 +199,13 @@ public R1RateDistribution smallerR1RateDistribution()
  final double t)
  throws Exception
  {
+ if (Double.isInfinite (
+ t
+ ))
+ {
+ return 0.;
+ }
+
  if (!supported (
  t
  ))
@@ -231,7 +238,7 @@ public R1RateDistribution smallerR1RateDistribution()
  @Override public double mean()
  throws Exception
  {
- return NewtonCotesQuadratureGenerator.GaussLaguerreRightDefinite (
+ return NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (
  0.,
  QUADRATURE_POINT_COUNT
  ).integrate (
@@ -251,12 +258,28 @@ public R1RateDistribution smallerR1RateDistribution()
  );
  }
 
+ @Override public double mode()
+ throws Exception
+ {
+ double largerRate = _largerR1RateDistribution.rate();
+
+ double smallerRate = _smallerR1RateDistribution.rate();
+
+ return largerRate == smallerRate ? 1. / largerRate : (
+ Math.log (
+ largerRate
+ ) - Math.log (
+ smallerRate
+ )
+ ) / (largerRate - smallerRate);
+ }
+
  @Override public double variance()
  throws Exception
  {
  final double mean = mean();
 
- return NewtonCotesQuadratureGenerator.GaussLaguerreRightDefinite (
+ return NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (
  0.,
  QUADRATURE_POINT_COUNT
  ).integrate (

diff --git a/src/main/java/org/drip/numerical/integration/AbscissaTransform.java b/src/main/java/org/drip/numerical/integration/AbscissaTransform.java
@@ -284,7 +284,7 @@ public static final AbscissaTransform GaussLaguerreLeftDefinite (
  @Override public double evaluate (
  final double x)
  {
- return left + (x / (1. - x));
+ return 1. == x ? left : left + (x / (1. - x));
  }
  },
  new org.drip.function.definition.R1ToR1 (null)

diff --git a/src/main/java/org/drip/sample/exponential/R1MinimumRateDistribution.java b/src/main/java/org/drip/sample/exponential/R1MinimumRateDistribution.java
@@ -1,6 +1,8 @@
 
 package org.drip.sample.exponential;
 
+import org.drip.measure.exponential.RealizedMinimaR1RateDistribution;
+import org.drip.service.common.FormatUtil;
 import org.drip.service.env.EnvManager;
 
 /*
@@ -131,6 +133,38 @@ public static final void main (
  {
  EnvManager.InitEnv ("");
 
+ double[] lambdaArray = {0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1., 2., 3., 4., 5.};
+
+ RealizedMinimaR1RateDistribution realizedMinimaR1RateDistribution =
+ RealizedMinimaR1RateDistribution.Standard (lambdaArray);
+
+ System.out.println ("\t||----------------------------------------------------------------------||");
+
+ System.out.println ("\t|| Realized R^1 Minimum Rate Distribution Likelihood ||");
+
+ System.out.println ("\t||----------------------------------------------------------------------||");
+
+ for (int i = 0; i < lambdaArray.length; ++i)
+ {
+ System.out.println (
+ "\t|| Index:" + FormatUtil.FormatDouble (i + 1, 2, 0, 1.) + "; Lambda:" +
+ FormatUtil.FormatDouble (lambdaArray[i], 1, 2, 1.) +
+ " => Probability as Realized Minimum:" + FormatUtil.FormatDouble (
+ realizedMinimaR1RateDistribution.probabilityOfIndexAsMinimum (i), 1, 6, 1.
+ ) + " ||"
+ );
+ }
+
+ System.out.println ("\t||----------------------------------------------------------------------||");
+
+ System.out.println (
+ "\t|| Realized R^1 Minimum Rate Distribution Lambda =>" + FormatUtil.FormatDouble (
+ realizedMinimaR1RateDistribution.lambda(), 2, 2, 1.
+ )
+ );
+
+ System.out.println ("\t||----------------------------------------------------------------------||");
+
  EnvManager.TerminateEnv();
  }
 }