com.numericalmethod.suanshu.stats.distribution.univariate
Class BetaDistribution

java.lang.Object
  com.numericalmethod.suanshu.stats.distribution.univariate.BetaDistribution

All Implemented Interfaces:

UnivariateDistribution

public class BetaDistribution
extends java.lang.Object
implements UnivariateDistribution

BetaDistribution distribution is the posterior distribution of the parameter p of a binomial distribution after observing α − 1 independent events with probability p and β − 1 with probability 1 − p, if the prior distribution of p is uniform.

The R equivalent functions are dbeta, pbeta, qbeta, rbeta.

See Also:

Wikipedia: BetaDistribution distribution

Field Summary

double	alpha α: the shape parameter
double	beta β: the shape parameter

Constructor Summary

BetaDistribution(double alpha, double beta)
Construct a Beta distribution.

Method Summary

double	ccdf(double x)
double	cdf(double x) The cumulative distribution function.
double	density(double x) The density function, which, if exists, is the derivative of F.
double	entropy() Get the entropy of this distribution.
double	kurtosis() Get the excess kurtosis of this distribution.
double	mean() Get the mean of this distribution.
double	median() Get the median of this distribution.
double	moment(double x) Deprecated. Not supported yet.
double	quantile(double u) 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

Field Detail

alpha

public final double alpha

α: the shape parameter

beta

public final double beta

β: the shape parameter

Constructor Detail

BetaDistribution

public BetaDistribution(double alpha,
                        double beta)

Construct a Beta distribution.

Parameters:

alpha - the degree of freedom

beta - the degree of freedom

Method Detail

mean

public double mean()

Description copied from interface: UnivariateDistribution

Get the mean of this distribution.

Specified by:

mean in interface UnivariateDistribution

Returns:

the mean

See Also:

Wikipedia: Expected value

median

public double median()

Description copied from interface: UnivariateDistribution

Get the median of this distribution.

Specified by:

median in interface UnivariateDistribution

Returns:

the median

See Also:

Wikipedia: Median

variance

public double variance()

Description copied from interface: UnivariateDistribution

Get the variance of this distribution.

Specified by:

variance in interface UnivariateDistribution

Returns:

the variance

See Also:

Wikipedia: Variance

skew

public double skew()

Description copied from interface: UnivariateDistribution

Get the skewness of this distribution.

Specified by:

skew in interface UnivariateDistribution

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

public double kurtosis()

Description copied from interface: UnivariateDistribution

Get the excess kurtosis of this distribution.

Specified by:

kurtosis in interface UnivariateDistribution

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

entropy

public double entropy()

Description copied from interface: UnivariateDistribution

Get the entropy of this distribution.

Specified by:

entropy in interface UnivariateDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

public double cdf(double x)

Description copied from interface: UnivariateDistribution

The cumulative distribution function.

F(x) = Pr(X <= x)

Specified by:

cdf in interface UnivariateDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X <= x)

See Also:

Wikipedia: Cumulative distribution function

ccdf

public double ccdf(double x)

density

public double density(double x)

Description copied from interface: UnivariateDistribution

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 UnivariateDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X <= x)

See Also:

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

quantile

public double quantile(double u)

Description copied from interface: UnivariateDistribution

The inverse of the cumulative distribution function. It returns the value below which random draws from the given 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 UnivariateDistribution

Parameters:

u - u

Returns:

F-1(u)

See Also:

Wikipedia: Quantile function

moment

@Deprecated
public double moment(double x)

Deprecated. Not supported yet.

Description copied from interface: UnivariateDistribution

The moment generating function, which is the expected value of

etX

This may not always exist.

Specified by:

moment in interface UnivariateDistribution

Parameters:

x - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function