Package org.drip.measure.chisquare

Class R1CentralCLTProxy

java.lang.Object

org.drip.measure.continuous.R1Distribution

org.drip.measure.chisquare.R1CentralCLTProxy

public class R1CentralCLTProxy
extends R1Distribution

R1CentralCLTProxy implements the N (0, 1) CLT Proxy Version for the R¹ Chi-Square Distribution. The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of Speech and Audio IEEE/ACM Transactions on Audio, Speech, and Language Processing 26 (1) 19-30
• Chi-Squared Distribution (2019): Chi-Squared Function https://en.wikipedia.org/wiki/Chi-squared_distribution
• Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): Continuous Univariate Distributions 2^nd Edition John Wiley and Sons
• National Institute of Standards and Technology (2019): Chi-Squared Distribution https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

It provides the following Functionality:

• R1CentralCLTProxy Constructor
• Retrieve the Degrees of Freedom
• Lay out the Support of the PDF Range
• Compute the Density under the Distribution at the given Variate
• Compute the cumulative under the distribution to the given value
• Retrieve the Mean of the Distribution
• Retrieve the Median of the Distribution
• Retrieve the Mode of the Distribution
• Retrieve the Variance of the Distribution
• Retrieve the Skewness of the Distribution
• Retrieve the Excess Kurtosis of the Distribution
• Retrieve the Differential Entropy of the Distribution
• Construct the Moment Generating Function
• Construct the Probability Generating Function
• Generate a Random Variable corresponding to the Distribution

Module	Computational Core Module
Library	Numerical Analysis Library
Project	Rd Continuous/Discrete Probability Measures
Package	Chi-Square Distribution Implementation/Properties

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1CentralCLTProxy(int degreesOfFreedom)	R1CentralCLTProxy Constructor

Method Summary

Modifier and Type	Method	Description
double	cumulative(double t)	Compute the cumulative under the distribution to the given value
int	degreesOfFreedom()	Retrieve the Degrees of Freedom
double	density(double t)	Compute the Density under the Distribution at the given Variate
double	differentialEntropy()	Retrieve the Differential Entropy of the Distribution
double	excessKurtosis()	Retrieve the Excess Kurtosis of the Distribution
double	mean()	Retrieve the Mean of the Distribution
double	median()	Retrieve the Median of the Distribution
double	mode()	Retrieve the Mode of the Distribution
R1ToR1	momentGeneratingFunction()	Construct the Moment Generating Function
R1ToR1	probabilityGeneratingFunction()	Construct the Probability Generating Function
double	random()	Generate a Random Variable corresponding to the Distribution
double	skewness()	Retrieve the Skewness of the 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, expectedShortfall, fisherInformation, histogram, incremental, invCumulative, iqr, kullbackLeiblerDivergence, nonCentralMoment, populationCentralMeasures, quantile, randomArray, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

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

Constructor Details

R1CentralCLTProxy

public R1CentralCLTProxy(int degreesOfFreedom)
                  throws java.lang.Exception

R1CentralCLTProxy Constructor

Parameters:

degreesOfFreedom - Degrees of Freedom

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

degreesOfFreedom

public int degreesOfFreedom()

Retrieve the Degrees of Freedom

Returns:

The Degrees of Freedom

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

cumulative

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

Compute the cumulative under the distribution to the given value

Specified by:

cumulative in class R1Distribution

Parameters:

t - Variate to which the cumulative is to be computed

Returns:

The cumulative

Throws:

java.lang.Exception - Thrown if the inputs are 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

median

public double median()
              throws java.lang.Exception

Retrieve the Median of the Distribution

Overrides:

median in class R1Distribution

Returns:

The Median of the Distribution

Throws:

java.lang.Exception - Thrown if the Median 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

skewness

public double skewness()
                throws java.lang.Exception

Retrieve the Skewness of the Distribution

Overrides:

skewness in class R1Distribution

Returns:

The Skewness of the Distribution

Throws:

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

excessKurtosis

public double excessKurtosis()
                      throws java.lang.Exception

Retrieve the Excess Kurtosis of the Distribution

Overrides:

excessKurtosis in class R1Distribution

Returns:

The Excess Kurtosis of the Distribution

Throws:

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

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

momentGeneratingFunction

public R1ToR1 momentGeneratingFunction()

Construct the Moment Generating Function

Overrides:

momentGeneratingFunction in class R1Distribution

Returns:

The Moment Generating Function

probabilityGeneratingFunction

public R1ToR1 probabilityGeneratingFunction()

Construct the Probability Generating Function

Overrides:

probabilityGeneratingFunction in class R1Distribution

Returns:

The Probability Generating Function

random

public double random()
              throws java.lang.Exception

Generate a Random Variable corresponding to the Distribution

Overrides:

random in class R1Distribution

Returns:

Random Variable corresponding to the Distribution

Throws:

java.lang.Exception - Thrown if the Random Instance cannot be estimated