Package dev.nm.stat.distribution.univariate

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). \[ F(x) = Pr(X invalid input: '<' x) \]
See Also:

  • 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
      See Also:

    • median

      double median()
      Gets the median of this distribution.
      Returns:
      the median
      See Also:

    • variance

      double variance()
      Gets the variance of this distribution.
      Returns:
      the variance
      See Also:

    • skew

      double skew()
      Gets the skewness of this distribution.
      Returns:
      the skewness
      See Also:

    • kurtosis

      double kurtosis()
      Gets the excess kurtosis of this distribution.
      Returns:
      the excess kurtosis
      See Also:

    • entropy

      double entropy()
      Gets the entropy of this distribution.
      Returns:
      the entropy
      See Also:

    • cdf

      double cdf(double x)
      Gets the cumulative probability F(x) = Pr(X ≤ x).
      Parameters:
      x - x
      Returns:
      F(x) = Pr(X ≤ x)
      See Also:

    • 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)
      See Also:

    • 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:

    • moment

      double moment(double t)
      The moment generating function is the expected value of etX. That is,
      E(etX)
      This may not always exist.
      Parameters:
      t - t
      Returns:
      E(exp(tX))
      See Also: