Package org.drip.measure.exponential

Class PoissonDistribution

java.lang.Object

org.drip.measure.continuous.R1Distribution

org.drip.measure.exponential.PoissonDistribution

public class PoissonDistribution
extends R1Distribution

PoissonDistribution implements the Univariate Poisson Distribution using the specified Mean/Variance. It provides the following Functionality:

• Construct a PoissonDistribution Instance
• Retrieve Lambda
• Lay out the Support of the PDF Range
• Compute the cumulative under the distribution to the given value
• Compute the inverse cumulative under the distribution corresponding to the given value
• Compute the Density under the Distribution at the given Variate
• Retrieve the Mean of the Distribution
• Retrieve the Variance of the Distribution
• Retrieve the Univariate Weighted Histogram

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
PoissonDistribution(double lambda)	Construct a PoissonDistribution Instance

Method Summary

Modifier and Type	Method	Description
double	cumulative(double x)	Compute the cumulative under the distribution to the given value
double	density(double x)	Compute the Density under the Distribution at the given Variate
Array2D	histogram()	Retrieve the Univariate Weighted Histogram
double	invCumulative(double y)	Compute the inverse cumulative under the distribution corresponding to the given value
double	lambda()	Retrieve Lambda
double	mean()	Retrieve the Mean 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, differentialEntropy, excessKurtosis, expectedShortfall, fisherInformation, incremental, iqr, kullbackLeiblerDivergence, median, mode, 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

PoissonDistribution

public PoissonDistribution(double lambda)
                    throws java.lang.Exception

Construct a PoissonDistribution Instance

Parameters:

lambda - Lambda

Throws:

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

Method Details

lambda

public double lambda()

Retrieve Lambda

Returns:

Lambda

support

public double[] support()

Lay out the Support of the PDF Range

Specified by:

support in class R1Distribution

Returns:

Support of the PDF Range

cumulative

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

Compute the cumulative under the distribution to the given value

Specified by:

cumulative in class R1Distribution

Parameters:

x - Variate to which the cumulative is to be computed

Returns:

The cumulative

Throws:

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

invCumulative

public double invCumulative(double y)
                     throws java.lang.Exception

Compute the inverse cumulative under the distribution corresponding to the given value

Overrides:

invCumulative in class R1Distribution

Parameters:

y - Value corresponding to which the inverse cumulative is to be computed

Returns:

The inverse cumulative

Throws:

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

density

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

Compute the Density under the Distribution at the given Variate

Specified by:

density in class R1Distribution

Parameters:

x - 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()

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

variance

public double variance()

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

histogram

public Array2D histogram()

Retrieve the Univariate Weighted Histogram

Overrides:

histogram in class R1Distribution

Returns:

The Univariate Weighted Histogram