smile.stat.distribution

Class FDistribution

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.FDistribution

All Implemented Interfaces:

java.io.Serializable, Distribution

public class FDistribution
extends AbstractDistribution

F-distribution arises in the testing of whether two observed samples have the same variance. A random variate of the F-distribution arises as the ratio of two chi-squared variates:

 U1 / d1
 -------
 U2 / d2
 

where U1 and U2 have chi-square distributions with d1 and d2 degrees of freedom respectively, and U1 and U2 are independent.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
int	nu1 The degrees of freedom of chi-square distribution in numerator.
int	nu2 The degrees of freedom chi-square distribution in denominator.

Constructor Summary

Constructors

Constructor and Description
FDistribution(int nu1, int nu2) Constructor.

Method Summary

Modifier and Type	Method and Description
double	cdf(double x) Cumulative distribution function.
double	entropy() Shannon entropy.
int	length() The number of parameters of the distribution.
double	logp(double x) The density at x in log scale, which may prevents the underflow problem.
double	mean() The mean of distribution.
double	p(double x) The probability density function for continuous distribution or probability mass function for discrete distribution at x.
double	quantile(double p) The quantile, the probability to the left of quantile is p.
double	rand() Generates a random number following this distribution.
java.lang.String	toString()
double	variance() The variance of distribution.

Methods inherited from class smile.stat.distribution.AbstractDistribution

inverseTransformSampling, quantile, quantile, rejection

Methods inherited from class java.lang.Object

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

Methods inherited from interface smile.stat.distribution.Distribution

likelihood, logLikelihood, rand, sd

Field Detail

nu1

public final int nu1

The degrees of freedom of chi-square distribution in numerator.

nu2

public final int nu2

The degrees of freedom chi-square distribution in denominator.

Constructor Detail

FDistribution

public FDistribution(int nu1,
                     int nu2)

Constructor.

Parameters:

nu1 - the degree of freedom of chi-square distribution in numerator.

nu2 - the degree of freedom of chi-square distribution in denominator.

Method Detail

length

public int length()

Description copied from interface: Distribution

The number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.

mean

public double mean()

Description copied from interface: Distribution

The mean of distribution.

variance

public double variance()

Description copied from interface: Distribution

The variance of distribution.

entropy

public double entropy()

Shannon entropy. Not supported.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

rand

public double rand()

Description copied from interface: Distribution

Generates a random number following this distribution.

p

public double p(double x)

Description copied from interface: Distribution

The probability density function for continuous distribution or probability mass function for discrete distribution at x.

logp

public double logp(double x)

Description copied from interface: Distribution

The density at x in log scale, which may prevents the underflow problem.

cdf

public double cdf(double x)

Description copied from interface: Distribution

Cumulative distribution function. That is the probability to the left of x.

quantile

public double quantile(double p)

Description copied from interface: Distribution

The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.