com.imsl.stat.distributions

Class ExponentialPD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.ExponentialPD

All Implemented Interfaces:

ClosedFormMaximumLikelihoodInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable

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

The exponential probability distribution.

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
ExponentialPD() Constructs an exponential probability distribution.

Method Summary

Modifier and Type	Method and Description
double[]	getClosedFormMLE(double[] x) Returns the closed form maximum likelihood estimates.
double[]	getClosedFormMlStandardError(double[] x) Returns the standard error based on the closed form maximum likelihood estimates.
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 of the pdf.
double	pdf(double x, double... params) Returns the value of the exponential 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

ExponentialPD

public ExponentialPD()

Constructs an exponential 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. b is strictly positive.

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. b is strictly positive.

pdf

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

Returns the value of the exponential probability density function.

The probability density function of the exponential distribution is $$f(x|b)=\Gamma\left(x|1,b\right)=\frac{1}{b}e^{-\frac{x}{b}}$$ where b is a scale parameter.

Specified by:

pdf in class ProbabilityDistribution

Parameters:

x - a double, the value (quantile) at which to evaluate the pdf. x must be non negative.

params - a double, the scale parameter.

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 array containing values of the parameter

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 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 array containing value of the parameter

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 estimates.

Specified by:

getClosedFormMLE in interface ClosedFormMaximumLikelihoodInterface

Parameters:

x - a double array containing the data

Returns:

a double array containing maximum likelihood estimates

getClosedFormMlStandardError

public double[] getClosedFormMlStandardError(double[] x)

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

Specified by:

getClosedFormMlStandardError in interface ClosedFormMaximumLikelihoodInterface

Parameters:

x - a double array containing the data

Returns:

a double array containing the standard errors