com.imsl.stat.distributions

Class LogNormalPD

java.lang.Object

com.imsl.stat.distributions.ProbabilityDistribution

com.imsl.stat.distributions.LogNormalPD

All Implemented Interfaces:

ClosedFormMaximumLikelihoodInterface, PDFGradientInterface, PDFHessianInterface, Serializable, Cloneable

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

The log-normal probability distribution.

See Also:

Example, Serialized Form

Constructor Summary

Constructors

Constructor and Description
LogNormalPD() Constructor for the log-normal 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 errors of the closed form maximum likelihood estimates.
double[]	getMethodOfMomentsEstimates(double[] x) Returns the method-of-moments estimates given the sample data.
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 evaluated at x.
double[][]	getPDFHessian(double x, double... params) Returns the analytic Hessian of the pdf evaluated at x.
double	pdf(double x, double... params) Returns the value of the 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

LogNormalPD

public LogNormalPD()

Constructor for the log-normal 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 for \(\mu\in\mathbb{R}\) and \(\sigma\gt0\)

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 for \(\mu\in\mathbb{R}\) and \(\sigma\gt0\)

pdf

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

Returns the value of the probability density function.

The probability density function of the log-normal distribution is $$f\left(x\right)=\frac{1}{x\sigma\sqrt{2\pi}} {e^{-\frac{{(\ln{x}-\mu)}^2 }{2{\sigma}^2}}}$$ where \(\mu\) is a location parameter and \(\sigma > 0\) is the scale parameter.

Specified by:

pdf in class ProbabilityDistribution

Parameters:

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

params - a double array containing the parameters. The parameters can also be given in the form pdf(x,a,b), where a=\(\mu\) and b=\(\sigma\) 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 evaluated at x.

Specified by:

getPDFGradient in interface PDFGradientInterface

Parameters:

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

params - a double array containing the parameters

Returns:

a double array containing the first partial derivatives of the pdf with respect to the parameters evaluated at x and the input values params

getPDFHessian

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

Returns the analytic Hessian of the pdf evaluated at x.

Specified by:

getPDFHessian in interface PDFHessianInterface

Parameters:

x - a double, the value at which to evaluate the Hessian. x must be strictly positive.

params - a double array containing the parameters, \(\mu\) and \(\sigma\).

Returns:

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

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 for \(\mu, \sigma\)

getClosedFormMlStandardError

public double[] getClosedFormMlStandardError(double[] x)

Returns the standard errors of 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 for the estimates of \(\mu, \sigma\)

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 estimates for \(\mu\) and \(\sigma\)