com.numericalmethod.suanshu.stats.distribution.univariate

Interface ProbabilityDistribution

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

ADFAsymptoticDistribution, ADFAsymptoticDistribution1, ADFDistribution, ADFFiniteSampleDistribution, BetaDistribution, BinomialDistribution, ChiSquareDistribution, EmpiricalDistribution, ExponentialDistribution, FDistribution, FisherExactDistribution, GammaDistribution, JarqueBeraDistribution, JohansenAsymptoticDistribution, KolmogorovDistribution, KolmogorovOneSidedDistribution, KolmogorovTwoSamplesDistribution, LogNormalDistribution, NormalDistribution, PoissonDistribution, RayleighDistribution, ShapiroWilkDistribution, TDistribution, WeibullDistribution, WilcoxonRankSumDistribution, WilcoxonSignedRankDistribution

public interface ProbabilityDistribution
extends java.io.Serializable

A univariate probability distribution completely characterizes a random variable by stipulating the probability of each value of a random variable (when the variable is discrete), or the probability of the value falling within a particular interval (when the variable is continuous).

F(x) = Pr(X &le x)

See Also:

Wikipedia: Probability 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() 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) 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.

Method Detail

mean

double mean()

Get the mean of this distribution.

Returns:

the mean

See Also:

Wikipedia: Expected value

median

double median()

Get the median of this distribution.

Returns:

the median

See Also:

Wikipedia: Median

variance

double variance()

Get the variance of this distribution.

Returns:

the variance

See Also:

Wikipedia: Variance

skew

double skew()

Get the skewness of this distribution.

Returns:

the skewness

See Also:

Wikipedia: Skewness

kurtosis

double kurtosis()

Get the excess kurtosis of this distribution.

Returns:

the excess kurtosis

See Also:

Wikipedia: Kurtosis

entropy

double entropy()

Get the entropy of this distribution.

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

cdf

double cdf(double x)

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

Parameters:

x - x

Returns:

F(x) = Pr(X ≤ x)

See Also:

Wikipedia: Cumulative distribution function

quantile

double quantile(double u)

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.

Parameters:

u - u, a quantile

Returns:

F^-1(u)

See Also:

Wikipedia: Quantile function

density

double density(double x)

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.

Parameters:

x - x

Returns:

f(x)

See Also:

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

moment

double moment(double x)

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

E(e^tX)

This may not always exist.

Parameters:

x - x

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function