com.imsl.stat.distributions

Class ContinuousUniformPD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.ContinuousUniformPD

All Implemented Interfaces:

ClosedFormMaximumLikelihoodInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable

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

The continuous uniform probability distribution.

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
ContinuousUniformPD() Constructs a continuous uniform 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 bounds of the parameters.
double[]	getParameterUpperBounds() Returns the upper bounds of the parameters.
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 continuous uniform 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

ContinuousUniformPD

public ContinuousUniformPD()

Constructs a continuous uniform probability distribution.

Method Detail

getParameterLowerBounds

public double[] getParameterLowerBounds()

Returns the lower bounds of the parameters.

Specified by:

getParameterLowerBounds in class ProbabilityDistribution

Returns:

a double array of length 2 containing the lower bounds (\( -\infty \lt a \lt b \lt \infty \))

getParameterUpperBounds

public double[] getParameterUpperBounds()

Returns the upper bounds of the parameters.

Specified by:

getParameterUpperBounds in class ProbabilityDistribution

Returns:

a double array of length 2 containing the upper bounds (\( -\infty \lt a \lt b \lt \infty \))

pdf

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

Returns the value of the continuous uniform probability density function.

The probability density function of the continuous uniform distribution is $$f(x|a,b)=\left\{\begin{array}{lll}\frac{1}{b-a}, & \mbox{for} & a\le x\le b \\ 0, & \mbox{for} & x\lt a \; \mbox{or} \; x\gt b \end{array}\right. $$ where \( -\infty \lt a \lt b \lt \infty \).

Specified by:

pdf in class ProbabilityDistribution

Parameters:

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

params - a double array containing the parameters a and b. The parameters can also be given in the form pdf(x,a,b), where a and b are scalars.

Returns:

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

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. The function is undefined when x = a or x = b.

params - a double array containing values of the parameters, a and b. The parameters can also be given in the form pdf(x,a,b), where a and b are scalars.

Returns:

a double array containing the first partial derivative of the pdf given the parameters

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. The function is undefined when x = a or x = b.

params - a double array containing values of the parameters, a and b. The parameters can also be given in the form pdf(x,a,b), where a and b are scalars.

Returns:

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

getClosedFormMLE

public double[] getClosedFormMLE(double[] x)

Returns the closed form maximum likelihood estimates.

For the continuous uniform distribution, the maximum likelihood estimates are the minimum and maximum of the sample data.

Specified by:

getClosedFormMLE in interface ClosedFormMaximumLikelihoodInterface

Parameters:

x - a double array containing the data

Returns:

a double array containing the closed form 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