com.numericalmethod.suanshu.stats.distribution.univariate

Class FDistribution

java.lang.Object

com.numericalmethod.suanshu.stats.distribution.univariate.FDistribution

All Implemented Interfaces:

ProbabilityDistribution, java.io.Serializable

public class FDistribution
extends java.lang.Object
implements ProbabilityDistribution

The F distribution is the distribution of the ratio of two independent chi-squared variates.

The R equivalent functions are df, pf, qf, rf.

See Also:

Wikipedia: FDistribution-distribution, Serialized Form

Constructor Summary

Constructors

Constructor and Description
FDistribution(double df1, double df2) Construct an F distribution.

Method Summary

Modifier and Type	Method and Description
double	cdf(double x) Get the cumulative probability F(x) = Pr(X ≤ x).
double	density(double x) The density function, which, if exists, is the derivative of F.
double	entropy() Deprecated. Not supported yet.
double	kurtosis() Get the excess kurtosis of this distribution.
double	mean() Get the mean of this distribution.
double	median() Deprecated. Not supported yet.
double	moment(double x) The moment generating function is the expected value of etX.
double	quantile(double u) Get the quantile, the inverse of the cumulative distribution function.
double	skew() Get the skewness of this distribution.
double	variance() Get the variance of this distribution.

Methods inherited from class java.lang.Object

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

Constructor Detail

FDistribution

public FDistribution(double df1,
                     double df2)

Construct an F distribution.

Parameters:

df1 - the first degree of freedom

df2 - the second degree of freedom

Method Detail

mean

public double mean()

Get the mean of this distribution.

Specified by:

mean in interface ProbabilityDistribution

Returns:

the mean

Throws:

java.lang.UnsupportedOperationException - when df2 ≤ 2

See Also:

Wikipedia: Expected value

median

@Deprecated
public double median()

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get the median of this distribution.

Specified by:

median in interface ProbabilityDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

public double variance()

Get the variance of this distribution.

Specified by:

variance in interface ProbabilityDistribution

Returns:

the variance

Throws:

java.lang.UnsupportedOperationException - when df2 ≤ 4

See Also:

Wikipedia: Variance

skew

public double skew()

Get the skewness of this distribution.

Specified by:

skew in interface ProbabilityDistribution

Returns:

the skewness

Throws:

java.lang.UnsupportedOperationException - when df2 ≤ 6

See Also:

Wikipedia: Skewness

kurtosis

public double kurtosis()

Get the excess kurtosis of this distribution.

Specified by:

kurtosis in interface ProbabilityDistribution

Returns:

the excess kurtosis

Throws:

java.lang.UnsupportedOperationException - when df2 ≤ 8

See Also:

Wikipedia: Kurtosis

entropy

@Deprecated
public double entropy()

Deprecated. Not supported yet.

Description copied from interface: ProbabilityDistribution

Get the entropy of this distribution.

Specified by:

entropy in interface ProbabilityDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

public double cdf(double x)

Description copied from interface: ProbabilityDistribution

Get the cumulative probability F(x) = Pr(X ≤ x).

Specified by:

cdf in interface ProbabilityDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X ≤ x)

See Also:

Wikipedia: Cumulative distribution function

density

public double density(double x)

Description copied from interface: ProbabilityDistribution

The density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space.

f(x) = dF(X) / dx

This may not always exist.

For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.

Specified by:

density in interface ProbabilityDistribution

Parameters:

x - x

Returns:

f(x)

See Also:

• Wikipedia: Probability density function
• Wikipedia: Probability mass function

quantile

public double quantile(double u)

Description copied from interface: ProbabilityDistribution

Get the quantile, the inverse of the cumulative distribution function. It is the value below which random draws from the distribution would fall u×100 percent of the time.

 F-1(u) = x, such that
 Pr(X ≤ x) = u
 

This may not always exist.

Specified by:

quantile in interface ProbabilityDistribution

Parameters:

u - u, a quantile

Returns:

F^-1(u)

See Also:

Wikipedia: Quantile function

moment

public double moment(double x)

Description copied from interface: ProbabilityDistribution

The moment generating function is the expected value of e^tX. That is,

E(e^tX)

This may not always exist.

Specified by:

moment in interface ProbabilityDistribution

Parameters:

x - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function