Class MaximaDistribution

  • All Implemented Interfaces:
    ProbabilityDistribution, UnivariateEVD

    public class MaximaDistribution
    extends Object
    implements UnivariateEVD
    The distribution of \(M\), where \(M=\max(x_1,x_2,...,x_n)\) and \(x_i\)'s are iid samples drawn from of a random variable \(X\) with cdf \(F(x)\). Since \(x_i\)'s are independent, the cumulative distribution function of \(M\) is simply \[ \begin{eqnarray} F_M(x;n) & = & Pr(\max(X_1,X_2,...,X_n) \le x) \\ & = & Pr(X_1 \le x, X_2 \le x, ..., X_n \le x) \\ & = & \prod_{i=1}^nF(x) \\ & = & [F(x)]^n \end{eqnarray} \]

    The R equivalent functions are evd::dextreme, evd::pextreme, evd::qextreme, evd::rextreme.

    • Constructor Summary

      Constructors 
      Constructor Description
      MaximaDistribution​(ProbabilityDistribution dist, int nIIDs)
      Create an instance with the probability distribution of \(X\), and the number of iid samples to be drawn.
    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double cdf​(double x)
      The cumulative distribution function.
      double density​(double x)
      The probability density function.
      double entropy()
      Gets the entropy of this distribution.
      double kurtosis()
      Gets the excess kurtosis of this distribution.
      double logDensity​(double x)
      Get the logarithm of the probability density function at \(x\), that is, \(\log(f(x))\).
      double mean()
      Gets the mean of this distribution.
      double median()
      Gets the median of this distribution.
      double moment​(double x)
      The moment generating function is the expected value of etX.
      double quantile​(double p)
      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.