# Interface ProbabilityDistribution

All Known Subinterfaces:
UnivariateEVD
All Known Implementing Classes:
ADFAsymptoticDistribution, ADFAsymptoticDistribution1, ADFDistribution, ADFFiniteSampleDistribution, BetaDistribution, BinomialDistribution, ChiSquareDistribution, EmpiricalDistribution, ExponentialDistribution, FDistribution, FisherExactDistribution, FrechetDistribution, GammaDistribution, GeneralizedEVD, GeneralizedParetoDistribution, GumbelDistribution, JarqueBeraDistribution, JohansenAsymptoticDistribution, KolmogorovDistribution, KolmogorovOneSidedDistribution, KolmogorovTwoSamplesDistribution, LogNormalDistribution, MaximaDistribution, MinimaDistribution, NormalDistribution, OrderStatisticsDistribution, PoissonDistribution, RayleighDistribution, ReversedWeibullDistribution, ShapiroWilkDistribution, TDistribution, TriangularDistribution, TruncatedNormalDistribution, WeibullDistribution, WilcoxonRankSumDistribution, WilcoxonSignedRankDistribution

public interface ProbabilityDistribution
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). $F(x) = Pr(X invalid input: '<' x)$
• ## Method Summary

Modifier and Type
Method
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()
Gets the entropy of this distribution.
double
kurtosis()
Gets the excess kurtosis of this distribution.
double
mean()
Gets the mean of this distribution.
double
median()
Gets the median of this distribution.
double
moment(double t)
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.
• ## Method Details

• ### mean

double mean()
Gets the mean of this distribution.
Returns:
the mean
• ### median

double median()
Gets the median of this distribution.
Returns:
the median
• ### variance

double variance()
Gets the variance of this distribution.
Returns:
the variance
• ### skew

double skew()
Gets the skewness of this distribution.
Returns:
the skewness
• ### kurtosis

double kurtosis()
Gets the excess kurtosis of this distribution.
Returns:
the excess kurtosis
• ### entropy

double entropy()
Gets the entropy of this distribution.
Returns:
the entropy
• ### cdf

double cdf(double x)
Gets the cumulative probability F(x) = Pr(X ≤ x).
Parameters:
x - x
Returns:
F(x) = Pr(X ≤ x)
• ### quantile

double quantile(double u)
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.
Parameters:
u - u, a quantile
Returns:
F-1(u)
• ### 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)
t - t