drasys.or.prob
Class NormalDistribution

java.lang.Object
  |
  +--drasys.or.prob.Distribution
        |
        +--drasys.or.prob.ContinuousDistribution
              |
              +--drasys.or.prob.NormalDistribution

public class NormalDistribution

extends ContinuousDistribution

implements ContinuousDistributionI

An implementation of the Normal probability distribution.

References:

The Art of Computer Programming: Seminumerical Algorithms (Vol 2, 3rd Ed)
    Donald Ervin Knuth; Hardcover
Numerical Recipes in C : The Art of Scientific Computing
    William H. Press, et al / Hardcover / Published 1993
Probability and Statistics
    Morris H. Degroot / Hardcover / Published 1986
Mathematical Statistics With Applications
    Dennis D. Wackerly, et al / Hardcover / Published 1996

See Also:

Serialized Form

Inner Class Summary
class	NormalDistribution.Cdf
class	NormalDistribution.Pdf

 

Constructor Summary

NormalDistribution()           Create normal distribution with mean = 0 and std = 1.

NormalDistribution(double mean, double std)           Create normal distribution with explicit mean and std.

NormalDistribution(double mean, double std, IntegrationI integration)           The argument integration will be used to compute the cdf from the pdf.

NormalDistribution(double mean, double std, IntegrationI integration, EquationSolutionI solver)           The argument integration will be used to compute the cdf from the pdf.

NormalDistribution(double mean, double std, long seed)           Create normal distribution with explicit parameters and set the random seed.

 

Method Summary
double	cdf(double x)           Computes the cdf by numerical integration using the pdf.
boolean	equals(java.lang.Object o)
double	function(double x)
double	getRandomScaler()           Returns a random number from the normal distribution.
double	inverseCdf(double probability)           Computes the inverse cdf from the cdf numerically.
double	mean()           Returns the mean of the distribution.
double	pdf(double x)           Returns the value of the probability distribution function at x;
double	probability(double x1, double x2)           Computes the the probability that x will be between x1 and x2 by numerical integration using the pdf.
void	setParameters(double mean, double std)           Sets the distribution parameters.
double	std()           Returns the standard deviation of the distribution.
java.lang.String	toString()
double	variance()           Returns the variance of the distribution.

 

Methods inherited from class drasys.or.prob.ContinuousDistribution

probability

 

Methods inherited from class drasys.or.prob.Distribution

getRandomMatrix, getRandomNumberGenerator, getRandomVector, setElements, setElements, setRandomNumberGenerator, setSeed

 

Methods inherited from class java.lang.Object

clone, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

 

Constructor Detail

NormalDistribution

public NormalDistribution()

Create normal distribution with mean = 0 and std = 1.

NormalDistribution

public NormalDistribution(double mean,
                          double std)

Create normal distribution with explicit mean and std.

NormalDistribution

public NormalDistribution(double mean,
                          double std,
                          long seed)

Create normal distribution with explicit parameters and set the random seed.

NormalDistribution

public NormalDistribution(double mean,
                          double std,
                          IntegrationI integration)

The argument integration will be used to compute the cdf from the pdf.

NormalDistribution

public NormalDistribution(double mean,
                          double std,
                          IntegrationI integration,
                          EquationSolutionI solver)

The argument integration will be used to compute the cdf from the pdf. The argument solver will be used to compute the inverse cdf from the cdf. Setting either integration or solver to null will cause the default to be used.

function

public double function(double x)

cdf

public double cdf(double x)

Computes the cdf by numerical integration using the pdf.

Throws:

StatError - if the integration fails.

inverseCdf

public double inverseCdf(double probability)

Computes the inverse cdf from the cdf numerically.

Specified by:

inverseCdf in interface ContinuousDistributionI

Overrides:

inverseCdf in class ContinuousDistribution

Throws:

StatError - if the solution fails.

probability

public double probability(double x1,
                          double x2)

Computes the the probability that x will be between x1 and x2 by numerical integration using the pdf.

Throws:

StatError - if the integration fails.

InvalidArgumentError - if x2 < x1.

setParameters

public void setParameters(double mean,
                          double std)

Sets the distribution parameters.

Throws:

InvalidArgumentError - if std <= 0.0.

pdf

public double pdf(double x)

Returns the value of the probability distribution function at x;

mean

public double mean()

Returns the mean of the distribution.

variance

public double variance()

Returns the variance of the distribution.

std

public double std()

Returns the standard deviation of the distribution.

getRandomScaler

public double getRandomScaler()

Returns a random number from the normal distribution.

Overrides:

getRandomScaler in class ContinuousDistribution

equals

public boolean equals(java.lang.Object o)

Overrides:

equals in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object