com.imsl.stat.distributions

Class NormalPD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.NormalPD

All Implemented Interfaces:

PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable

public class NormalPD
extends ProbabilityDistribution
implements PDFHessianInterface, Serializable, Cloneable

The normal (Gaussian) probability distribution

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
NormalPD() Constructor for the normal probability distribution

Method Summary

Methods

Modifier and Type	Method and Description
double[]	getMLEs(double[] x) Returns the mean and standard deviation of the sample data.
double[]	getParameterLowerBounds() Returns the lower bounds for the mean and standard deviation .
double[]	getParameterUpperBounds() Returns the upper bounds for the mean and standard deviation .
double[]	getPDFGradient(double x, double[] params) Returns the analytic gradient of the normal pdf.
double[][]	getPDFHessian(double x, double[] params) Returns the analytic hessian matrix of the normal pdf evaluated at a point, x.
double	pdf(double x, double[] params) Returns the value of the normal 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

NormalPD

public NormalPD()

Constructor for the normal probability distribution

Method Detail

getMLEs

public double[] getMLEs(double[] x)

Returns the mean and standard deviation of the sample data.

These are the maximum likelihood estimates for the mean and standard deviation of the Normal distribution, given the data.

Parameters:

x - a double array containing the data

Returns:

a double array containing the mean and standard deviation

getParameterLowerBounds

public double[] getParameterLowerBounds()

Returns the lower bounds for the mean and standard deviation .

Specified by:

getParameterLowerBounds in class ProbabilityDistribution

Returns:

a double array containing the lower bounds

getParameterUpperBounds

public double[] getParameterUpperBounds()

Returns the upper bounds for the mean and standard deviation .

Specified by:

getParameterUpperBounds in class ProbabilityDistribution

Returns:

a double array containing the upper bounds

getPDFGradient

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

Returns the analytic gradient of the normal pdf.

Specified by:

getPDFGradient in interface PDFGradientInterface

Parameters:

x - a double value

params - a double array containing values of the parameters, params[0]="" and params[1]="". The argument can also be a comma-delimited list "", "" or params[0], params[1].

Note: The argument params is a variable length argument list (varargs).

Returns:

a double array containing the partial derivatives of the pdf with respect to the parameters evaluated at x and the given parameter values

getPDFHessian

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

Returns the analytic hessian matrix of the normal pdf evaluated at a point, x.

Specified by:

getPDFHessian in interface PDFHessianInterface

Parameters:

x - a double value

params - a double array containing values of the parameters, params[0]="" and params[1]="". The argument can also be a comma-delimited list "", "" or params[0], params[1].

Note: The argument params is a variable length argument list (varargs).

Returns:

a double matrix containing the second partial derivatives of the pdf with respect to the parameters evaluated at x and the given parameter values

pdf

public double pdf(double x,
         double[] params)

Returns the value of the normal probability density function.

The probability density function for a normal distribution is given by

where and are the mean and standard deviation of the random variable.

Specified by:

pdf in class ProbabilityDistribution

Parameters:

x - a double value

params - a double array containing values of the parameters, params[0]="" and params[1]="". The argument can also be a comma-delimited list "", "" or params[0], params[1].

Note: The argument params is a variable length argument list (varargs).

Returns:

a double value equal to the probability density at x given the parameter values