com.imsl.stat.distributions

Class GeometricPD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.GeometricPD

All Implemented Interfaces:

ClosedFormMaximumLikelihoodInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable

public class GeometricPD
extends ProbabilityDistribution
implements Serializable, Cloneable, PDFHessianInterface, ClosedFormMaximumLikelihoodInterface

The geometric probability distribution.

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
GeometricPD() Constructor for the geometric probability distribution.

Method Summary

Modifier and Type	Method and Description
double[]	getClosedFormMLE(double[] x) Returns the maximum likelihood estimate for the parameter.
double[]	getClosedFormMlStandardError(double[] x) Returns the standard error of the maximum likelihood estimate.
double[]	getMethodOfMomentsEstimates(double[] x) Returns the method-of-moments estimates given the sample data.
double[]	getParameterLowerBounds() Returns the lower bound of the parameter.
double[]	getParameterUpperBounds() Returns the upper bound of the parameter.
double[]	getPDFGradient(double x, double... params) Returns the analytic gradient of the pdf evaluated at x.
double[][]	getPDFHessian(double x, double... params) Returns the analytic Hessian matrix evaluated at x.
double	pdf(double x, double... params) Returns the value of the geometric probability density function.

Methods inherited from class com.imsl.stat.distributions.ProbabilityDistribution

getNumberOfParameters, getPDFGradientApproximation, getPDFHessianApproximation, getRangeOfX, setRangeOfX

Methods inherited from class java.lang.Object

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

Constructor Detail

GeometricPD

public GeometricPD()

Constructor for the geometric probability distribution.

Method Detail

getParameterLowerBounds

public double[] getParameterLowerBounds()

Returns the lower bound of the parameter.

Specified by:

getParameterLowerBounds in class ProbabilityDistribution

Returns:

a double array of length 1 containing the lower bound (0)

getParameterUpperBounds

public double[] getParameterUpperBounds()

Returns the upper bound of the parameter.

Specified by:

getParameterUpperBounds in class ProbabilityDistribution

Returns:

a double array of length 1 containing the upper bound (1.0)

pdf

public double pdf(double x,
                  double... params)

Returns the value of the geometric probability density function.

Given the probability of success \(p\) for a sequence of independent and identical trials, the probability of \(X = k \in {0,1,2,\ldots }\) failures until the first success is given by \(Pr[X=k]=(1-p)^k p \). The discrete random variable \(X\) is a geometric random variable with parameter \(p\).

Specified by:

pdf in class ProbabilityDistribution

Parameters:

x - a double, the value (quantile) at which to evaluate the pdf. x must be a non-negative integer. If x is not a whole number the floor() value will be used.

params - a double, the probability of success

Returns:

a double, the probability density at x given the parameter value

getPDFGradient

public double[] getPDFGradient(double x,
                               double... params)

Returns the analytic gradient of the pdf evaluated at x.

Specified by:

getPDFGradient in interface PDFGradientInterface

Parameters:

x - a double value. x must be a non-negative integer. If x is not a whole number the floor() value will be used.

params - a double specifying the probability of success

Returns:

a double array containing the first partial derivative of the parameters

getPDFHessian

public double[][] getPDFHessian(double x,
                                double... params)

Returns the analytic Hessian matrix evaluated at x.

Specified by:

getPDFHessian in interface PDFHessianInterface

Parameters:

x - a double value. x must be a non-negative integer. If x is not a whole number the floor() value will be used.

params - a double specifying the probability of success

Returns:

a double matrix containing the second partial derivatives of the parameters

getClosedFormMLE

public double[] getClosedFormMLE(double[] x)

Returns the maximum likelihood estimate for the parameter.

Specified by:

getClosedFormMLE in interface ClosedFormMaximumLikelihoodInterface

Parameters:

x - a double array containing the data

Returns:

a double array containing the maximum likelihood estimate(s)

getClosedFormMlStandardError

public double[] getClosedFormMlStandardError(double[] x)

Returns the standard error of the maximum likelihood estimate.

Specified by:

getClosedFormMlStandardError in interface ClosedFormMaximumLikelihoodInterface

Parameters:

x - a double array containing the data

Returns:

a double array containing the standard errors

getMethodOfMomentsEstimates

public double[] getMethodOfMomentsEstimates(double[] x)

Returns the method-of-moments estimates given the sample data.

Parameters:

x - a double array containing the data

Returns:

a double array containing method-of-moments estimate(s)