# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.stats.distribution.univariate

## Class FDistribution

• java.lang.Object
• com.numericalmethod.suanshu.stats.distribution.univariate.FDistribution
• All Implemented Interfaces:
ProbabilityDistribution

public class FDistribution
extends 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.

Wikipedia: FDistribution-distribution
• ### Constructor Summary

Constructors
Constructor and Description
FDistribution(double df1, double df2)
Construct an F distribution.
• ### Method Summary

All Methods
Modifier and Type Method and Description
double cdf(double x)
Gets 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()
Gets the excess kurtosis of this distribution.
double mean()
Gets 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)
Gets the quantile, the inverse of the cumulative distribution function.
double skew()
Gets the skewness of this distribution.
double variance()
Gets 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()
Gets the mean of this distribution.
Specified by:
mean in interface ProbabilityDistribution
Returns:
the mean
Throws:
UnsupportedOperationException - when df2 ≤ 2
Wikipedia: Expected value
• #### median

@Deprecated
public double median()
Deprecated. Not supported yet.
Description copied from interface: ProbabilityDistribution
Gets the median of this distribution.
Specified by:
median in interface ProbabilityDistribution
Returns:
the median
Wikipedia: Median
• #### variance

public double variance()
Gets the variance of this distribution.
Specified by:
variance in interface ProbabilityDistribution
Returns:
the variance
Throws:
UnsupportedOperationException - when df2 ≤ 4
Wikipedia: Variance
• #### skew

public double skew()
Gets the skewness of this distribution.
Specified by:
skew in interface ProbabilityDistribution
Returns:
the skewness
Throws:
UnsupportedOperationException - when df2 ≤ 6
Wikipedia: Skewness
• #### kurtosis

public double kurtosis()
Gets the excess kurtosis of this distribution.
Specified by:
kurtosis in interface ProbabilityDistribution
Returns:
the excess kurtosis
Throws:
UnsupportedOperationException - when df2 ≤ 8
Wikipedia: Kurtosis
• #### entropy

@Deprecated
public double entropy()
Deprecated. Not supported yet.
Description copied from interface: ProbabilityDistribution
Gets the entropy of this distribution.
Specified by:
entropy in interface ProbabilityDistribution
Returns:
the entropy
Wikipedia: Entropy (information theory)
• #### cdf

public double cdf(double x)
Description copied from interface: ProbabilityDistribution
Gets the cumulative probability F(x) = Pr(X ≤ x).
Specified by:
cdf in interface ProbabilityDistribution
Parameters:
x - x
Returns:
F(x) = Pr(X ≤ x)
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)
• #### quantile

public double quantile(double u)
Description copied from interface: ProbabilityDistribution
Gets 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)
Wikipedia: Quantile function
• #### moment

public double moment(double x)
Description copied from interface: ProbabilityDistribution
The moment generating function is the expected value of etX. That is,
E(etX)
This may not always exist.
Specified by:
moment in interface ProbabilityDistribution
Parameters:
x - t
Returns:
E(exp(tX))