UnivariateDistribution (SuanShu 1.3.1 API Documentation)

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com.numericalmethod.suanshu.stats.distribution.univariate
Interface UnivariateDistribution

All Known Implementing Classes:: AdfAsymptoticDistribution, AdfAsymptoticDistribution1, AdfDistribution, AdfFiniteSampleDistribution, BetaDistribution, ChiSquareDistribution, EmpiricalDistribution, ExponentialDistribution, FDistribution, FisherExactDistribution, GammaDistribution, JarqueBeraDistribution, JohansenAsymptoticDistribution, KolmogorovDistribution, KolmogorovOneSidedDistribution, KolmogorovTwoSamplesDistribution, NormalDistribution, RayleighDistribution, ShapiroWilkDistribution, TDistribution, WeibullDistribution, WilcoxonRankSumDistribution, WilcoxonSignedRankDistribution

public interface UnivariateDistribution

A univariate 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 ≤ x)

See Also:: Wikipedia: Probability distribution

Method Summary
`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)` The moment generating function, which is the expected value of `e^tX` This may not always exist.
`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.

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)

The cumulative distribution function.

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)

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.

Parameters:: u - u
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: