Package org.drip.measure.exponential

Class RealizedMinimaR1RateDistribution

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.exponential.R1RateDistribution

org.drip.measure.exponential.RealizedMinimaR1RateDistribution

public class RealizedMinimaR1RateDistribution
extends R1RateDistribution

RealizedMinimaR1RateDistribution implements the Rate Parameterization of the Realized Minimum among the Set of R¹ Exponential Distributions. 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

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d Continuous/Discrete Probability Measures
• Package = R¹ Exponential Distribution Implementation/Properties

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	probabilityOfIndexAsMinimum(int index)	Calculate the Probability that the specified Index corresponds to the Realized Minimum
R1RateDistribution[]	r1RateDistributionArray()	Retrieve the R1 Exponential Distribution Array
static RealizedMinimaR1RateDistribution	Standard(double[] lambdaArray)	Standard Instance of RealizedMinimaR1RateDistribution

Methods inherited from class org.drip.measure.exponential.R1RateDistribution

bPOE, centralMoment, cumulative, cvar, density, excessKurtosis, fisherInformation, iqr, kullbackLeiblerDivergence, lambda, mean, median, mode, momentGeneratingFunction, nonCentralMoment, quantile, rate, scale, ScaleStandard, skewness, support, variance

Methods inherited from class org.drip.measure.continuous.R1Univariate

differentialEntropy, expectedShortfall, histogram, incremental, invCumulative, populationCentralMeasures, probabilityGeneratingFunction, random, randomArray, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

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

Method Details

Standard

public static final RealizedMinimaR1RateDistribution Standard(double[] lambdaArray)

Standard Instance of RealizedMinimaR1RateDistribution

Parameters:

lambdaArray - Array of the Distribution Lambdas

Returns:

Standard Instance of RealizedMinimaR1RateDistribution

r1RateDistributionArray

public R1RateDistribution[] r1RateDistributionArray()

Retrieve the R¹ Exponential Distribution Array

Returns:

The R¹ Exponential Distribution Array

probabilityOfIndexAsMinimum

public double probabilityOfIndexAsMinimum(int index)
                                   throws java.lang.Exception

Calculate the Probability that the specified Index corresponds to the Realized Minimum

Parameters:

index - Specified Index

Returns:

Probability that the specified Index corresponds to the Realized Minimum

Throws:

java.lang.Exception - Thrown if the Index cannot be calculated