com.imsl.stat.distributions

Class RayleighPD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.RayleighPD

All Implemented Interfaces:

ClosedFormMaximumLikelihoodInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable

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

The Rayleigh probability distribution.

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
RayleighPD() Constructor for the Rayleigh probability distribution.

Method Summary

Modifier and Type	Method and Description
double[]	getClosedFormMLE(double[] x) Returns the closed form maximum likelihood estimate.
double[]	getClosedFormMlStandardError(double[] x) Returns the standard error based on the closed form maximum likelihood estimate.
double[]	getMethodOfMomentsEstimates(double[] x) Returns the method-of-moments estimate given the sample data.
double[]	getParameterLowerBounds() Returns the lower bound for the parameter.
double[]	getParameterUpperBounds() Returns the upper bound for the parameter.
double[]	getPDFGradient(double x, double... params) Returns the analytic gradient of the pdf.
double[][]	getPDFHessian(double x, double... params) Returns the analytic Hessian matrix of the pdf.
double	pdf(double x, double... params) Returns the value of the Rayleigh 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

RayleighPD

public RayleighPD()

Constructor for the Rayleigh probability distribution.

Method Detail

getParameterLowerBounds

public double[] getParameterLowerBounds()

Returns the lower bound for the parameter.

Specified by:

getParameterLowerBounds in class ProbabilityDistribution

Returns:

a double array of length 1 containing the lower bound for \(\sigma>0\)

getParameterUpperBounds

public double[] getParameterUpperBounds()

Returns the upper bound for the parameter.

Specified by:

getParameterUpperBounds in class ProbabilityDistribution

Returns:

a double array of length 1 containing the upper bound for \(\sigma>0\)

pdf

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

Returns the value of the Rayleigh probability density function.

The probability density function of the Rayleigh distribution is $$f\left(x;\sigma\right)=\begin{array}{ll} \frac{x}{\sigma^2}e^{-x^2/\left(2\sigma^2\right)}, & x\ge0 \end{array}$$ where \(\sigma > 0\) is the scale parameter.

Specified by:

pdf in class ProbabilityDistribution

Parameters:

x - a double, the value (quantile) at which to evaluate the pdf

params - a double, the scale parameter (\(\sigma\gt 0\))

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.

Specified by:

getPDFGradient in interface PDFGradientInterface

Parameters:

x - a double, the value at which to evaluate the gradient. x must be non-negative.

params - a double, the scale parameter (\(\sigma\gt 0\))

Returns:

a double array containing the first partial derivative of the pdf with respect to the parameter

getPDFHessian

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

Returns the analytic Hessian matrix of the pdf.

Specified by:

getPDFHessian in interface PDFHessianInterface

Parameters:

x - a double, the value at which to evaluate the Hessian. x must be non-negative.

params - a double, the scale parameter (\(\sigma\gt 0\))

Returns:

a double matrix containing the second partial derivatives of the pdf with respect to the parameter

getClosedFormMLE

public double[] getClosedFormMLE(double[] x)

Returns the closed form maximum likelihood estimate.

Specified by:

getClosedFormMLE in interface ClosedFormMaximumLikelihoodInterface

Parameters:

x - a double array containing the data

Returns:

a double array containing the maximum likelihood estimate

getClosedFormMlStandardError

public double[] getClosedFormMlStandardError(double[] x)

Returns the standard error based on the closed form maximum likelihood estimate.

Specified by:

getClosedFormMlStandardError in interface ClosedFormMaximumLikelihoodInterface

Parameters:

x - a double array containing the data

Returns:

a double array containing the standard error

getMethodOfMomentsEstimates

public double[] getMethodOfMomentsEstimates(double[] x)

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

Parameters:

x - a double array containing the data

Returns:

a double array containing method-of-moments estimate for the parameter