Package org.drip.measure.exponential
Class TwoIIDSum
java.lang.Object
org.drip.measure.continuous.R1Univariate
org.drip.measure.exponential.TwoIIDSum
public class TwoIIDSum extends R1Univariate
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 4th 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
- Module = Computational Core Module
- Library = Numerical Analysis Library
- Project = Rd Continuous/Discrete Probability Measures
- Package = R1 Exponential Distribution Implementation/Properties
- Author:
- Lakshmi Krishnamurthy
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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 valuedouble
density(double t)
Compute the Density under the Distribution at the given Variatedouble
differentialEntropy()
Retrieve the Differential Entropy of the DistributionR1RateDistribution
largerR1RateDistribution()
Retrieve the Larger Exponential Distributiondouble
mean()
Retrieve the Mean of the Distributiondouble
mode()
Retrieve the Mode of the DistributionR1RateDistribution
smallerR1RateDistribution()
Retrieve the Smaller Exponential Distributiondouble[]
support()
Lay out the Support of the PDF Rangedouble
variance()
Retrieve the Variance of the DistributionMethods inherited from class org.drip.measure.continuous.R1Univariate
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
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Constructor Details
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TwoIIDSum
public TwoIIDSum(R1RateDistribution firstR1RateDistribution, R1RateDistribution secondR1RateDistribution) throws java.lang.ExceptionTwoIIDSum Constructor- Parameters:
firstR1RateDistribution
- First R1 Exponential DistributionsecondR1RateDistribution
- Second R1 Exponential Distribution- Throws:
java.lang.Exception
- Thrown if Inputs are Invalid
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Method Details
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largerR1RateDistribution
Retrieve the Larger Exponential Distribution- Returns:
- The Larger Exponential Distribution
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smallerR1RateDistribution
Retrieve the Smaller Exponential Distribution- Returns:
- The Smaller Exponential Distribution
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support
public double[] support()Description copied from class:R1Univariate
Lay out the Support of the PDF Range- Specified by:
support
in classR1Univariate
- Returns:
- Support of the PDF Range
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density
public double density(double t) throws java.lang.ExceptionDescription copied from class:R1Univariate
Compute the Density under the Distribution at the given Variate- Specified by:
density
in classR1Univariate
- Parameters:
t
- Variate at which the Density needs to be computed- Returns:
- The Density
- Throws:
java.lang.Exception
- Thrown if the input is invalid
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mean
public double mean() throws java.lang.ExceptionDescription copied from class:R1Univariate
Retrieve the Mean of the Distribution- Specified by:
mean
in classR1Univariate
- Returns:
- The Mean of the Distribution
- Throws:
java.lang.Exception
- Thrown if the Mean cannot be estimated
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mode
public double mode() throws java.lang.ExceptionDescription copied from class:R1Univariate
Retrieve the Mode of the Distribution- Overrides:
mode
in classR1Univariate
- Returns:
- The Mode of the Distribution
- Throws:
java.lang.Exception
- Thrown if the Mode cannot be estimated
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variance
public double variance() throws java.lang.ExceptionDescription copied from class:R1Univariate
Retrieve the Variance of the Distribution- Specified by:
variance
in classR1Univariate
- Returns:
- The Variance of the Distribution
- Throws:
java.lang.Exception
- Thrown if the Variance cannot be estimated
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cumulative
public double cumulative(double upper) throws java.lang.ExceptionDescription copied from class:R1Univariate
Compute the cumulative under the distribution to the given value- Specified by:
cumulative
in classR1Univariate
- Parameters:
upper
- Variate to which the cumulative is to be computed- Returns:
- The cumulative
- Throws:
java.lang.Exception
- Thrown if the inputs are invalid
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differentialEntropy
public double differentialEntropy() throws java.lang.ExceptionDescription copied from class:R1Univariate
Retrieve the Differential Entropy of the Distribution- Overrides:
differentialEntropy
in classR1Univariate
- Returns:
- The Differential Entropy of the Distribution
- Throws:
java.lang.Exception
- Thrown if the Entropy cannot be estimated
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