sim.util.distribution
Class StudentT

java.lang.Object
  sim.util.distribution.AbstractDistribution
      sim.util.distribution.AbstractContinousDistribution
          sim.util.distribution.StudentT

All Implemented Interfaces:

java.io.Serializable

public class StudentT
extends AbstractContinousDistribution

StudentT distribution (aka T-distribution); See the math definition and animated definition.

p(x) = k * (1+x^2/f) ^ -(f+1)/2 where k = g((f+1)/2) / (sqrt(pi*f) * g(f/2)) and g(a) being the gamma function and f being the degrees of freedom.

Valid parameter ranges: freedom > 0.

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Implementation:

Method: Adapted Polar Box-Muller transformation.

This is a port of RandStudentT used in CLHEP 1.4.0 (C++). CLHEP's implementation, in turn, is based on tpol.c from the C-RAND / WIN-RAND library. C-RAND's implementation, in turn, is based upon

R.W. Bailey (1994): Polar generation of random variates with the t-distribution, Mathematics of Computation 62, 779-781.

See Also:

Serialized Form

Field Summary

protected double	freedom
protected double	TERM

Fields inherited from class sim.util.distribution.AbstractDistribution

randomGenerator

Constructor Summary

StudentT(double freedom, MersenneTwisterFast randomGenerator)
Constructs a StudentT distribution.

Method Summary

double	cdf(double x) Returns the cumulative distribution function.
double	nextDouble() Returns a random number from the distribution.
double	nextDouble(double degreesOfFreedom) Returns a random number from the distribution; bypasses the internal state.
double	pdf(double x) Returns the probability distribution function.
void	setState(double freedom) Sets the distribution parameter.
java.lang.String	toString() Returns a String representation of the receiver.

Methods inherited from class sim.util.distribution.AbstractDistribution

apply, apply, getRandomGenerator, nextInt, setRandomGenerator

Methods inherited from class java.lang.Object

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

Field Detail

freedom

protected double freedom

TERM

protected double TERM

Constructor Detail

StudentT

public StudentT(double freedom,
                MersenneTwisterFast randomGenerator)

Constructs a StudentT distribution. Example: freedom=1.0.

Parameters:

freedom - degrees of freedom.

Throws:

java.lang.IllegalArgumentException - if freedom <= 0.0.

Method Detail

cdf

public double cdf(double x)

Returns the cumulative distribution function.

nextDouble

public double nextDouble()

Returns a random number from the distribution.

Specified by:

nextDouble in class AbstractDistribution

nextDouble

public double nextDouble(double degreesOfFreedom)

Returns a random number from the distribution; bypasses the internal state.

Parameters:

a - degrees of freedom.

Throws:

java.lang.IllegalArgumentException - if a <= 0.0.

pdf

public double pdf(double x)

Returns the probability distribution function.

setState

public void setState(double freedom)

Sets the distribution parameter.

Parameters:

freedom - degrees of freedom.

Throws:

java.lang.IllegalArgumentException - if freedom <= 0.0.

toString

public java.lang.String toString()

Returns a String representation of the receiver.

Overrides:

toString in class java.lang.Object