Package org.drip.measure.exponential

Class TwoIIDSum

java.lang.Object

org.drip.measure.continuous.R1Distribution

org.drip.measure.exponential.TwoIIDSum

public class TwoIIDSum
extends R1Distribution

TwoIIDSum implements the PDF of the Sum of Two IID Exponential Random Variables. The References are:

• Devroye, L. (1986): Non-Uniform Random Variate Generation Springer-Verlag New York
• Exponential Distribution (2019): Exponential Distribution https://en.wikipedia.org/wiki/Exponential_distribution
• Norton, M., V. Khokhlov, and S. Uryasev (2019): Calculating CVaR and bPOE for Common Probability Distributions with Application to Portfolio Optimization and Density Estimation Annals of Operations Research 299 (1-2) 1281-1315
• Ross, S. M. (2009): Introduction to Probability and Statistics for Engineers and Scientists 4^th Edition Associated Press New York, NY
• Schmidt, D. F., and D. Makalic (2009): Universal Models for the Exponential Distribution IEEE Transactions on Information Theory 55 (7) 3087-3090

It provides the following Functionality:

• TwoIIDSum Constructor
• Retrieve the Larger Exponential Distribution
• Retrieve the Smaller Exponential Distribution
• Lay out the Support of the PDF Range
• Compute the Density under the Distribution at the given Variate
• Retrieve the Mean of the Distribution
• Retrieve the Mode of the Distribution
• Retrieve the Variance of the Distribution
• Compute the cumulative under the distribution to the given value
• Retrieve the Differential Entropy of the Distribution

Module	Computational Core Module
Library	Numerical Analysis Library
Project	Rd Continuous/Discrete Probability Measures
Package	R1 and Rd Continuous Random Measure

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
TwoIIDSum(R1RateDistribution firstR1RateDistribution, R1RateDistribution secondR1RateDistribution)	TwoIIDSum Constructor

Method Summary

Modifier and Type	Method	Description
double	cumulative(double upper)	Compute the cumulative under the distribution to the given value
double	density(double t)	Compute the Density under the Distribution at the given Variate
double	differentialEntropy()	Retrieve the Differential Entropy of the Distribution
R1RateDistribution	largerR1RateDistribution()	Retrieve the Larger Exponential Distribution
double	mean()	Retrieve the Mean of the Distribution
double	mode()	Retrieve the Mode of the Distribution
R1RateDistribution	smallerR1RateDistribution()	Retrieve the Smaller Exponential Distribution
double[]	support()	Lay out the Support of the PDF Range
double	variance()	Retrieve the Variance of the Distribution

Methods inherited from class org.drip.measure.continuous.R1Distribution

bPOE, centralMoment, cvar, excessKurtosis, expectedShortfall, fisherInformation, histogram, incremental, invCumulative, iqr, kullbackLeiblerDivergence, median, momentGeneratingFunction, nonCentralMoment, populationCentralMeasures, probabilityGeneratingFunction, quantile, random, randomArray, skewness, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

TwoIIDSum

public TwoIIDSum(R1RateDistribution firstR1RateDistribution,
R1RateDistribution secondR1RateDistribution)
          throws java.lang.Exception

TwoIIDSum Constructor

Parameters:

firstR1RateDistribution - First R¹ Exponential Distribution

secondR1RateDistribution - Second R¹ Exponential Distribution

Throws:

java.lang.Exception - Thrown if Inputs are Invalid

Method Details

largerR1RateDistribution

public R1RateDistribution largerR1RateDistribution()

Retrieve the Larger Exponential Distribution

Returns:

The Larger Exponential Distribution

smallerR1RateDistribution

public R1RateDistribution smallerR1RateDistribution()

Retrieve the Smaller Exponential Distribution

Returns:

The Smaller Exponential Distribution

support

public double[] support()

Lay out the Support of the PDF Range

Specified by:

support in class R1Distribution

Returns:

Support of the PDF Range

density

public double density(double t)
               throws java.lang.Exception

Compute the Density under the Distribution at the given Variate

Specified by:

density in class R1Distribution

Parameters:

t - Variate at which the Density needs to be computed

Returns:

The Density

Throws:

java.lang.Exception - Thrown if the input is invalid

mean

public double mean()
            throws java.lang.Exception

Retrieve the Mean of the Distribution

Specified by:

mean in class R1Distribution

Returns:

The Mean of the Distribution

Throws:

java.lang.Exception - Thrown if the Mean cannot be estimated

mode

public double mode()
            throws java.lang.Exception

Retrieve the Mode of the Distribution

Overrides:

mode in class R1Distribution

Returns:

The Mode of the Distribution

Throws:

java.lang.Exception - Thrown if the Mode cannot be estimated

variance

public double variance()
                throws java.lang.Exception

Retrieve the Variance of the Distribution

Specified by:

variance in class R1Distribution

Returns:

The Variance of the Distribution

Throws:

java.lang.Exception - Thrown if the Variance cannot be estimated

cumulative

public double cumulative(double upper)
                  throws java.lang.Exception

Compute the cumulative under the distribution to the given value

Specified by:

cumulative in class R1Distribution

Parameters:

upper - Variate to which the cumulative is to be computed

Returns:

The cumulative

Throws:

java.lang.Exception - Thrown if the inputs are invalid

differentialEntropy

public double differentialEntropy()
                           throws java.lang.Exception

Retrieve the Differential Entropy of the Distribution

Overrides:

differentialEntropy in class R1Distribution

Returns:

The Differential Entropy of the Distribution

Throws:

java.lang.Exception - Thrown if the Entropy cannot be estimated