Package jline.api.fj

Class FJ_xmax

java.lang.Object
jline.api.fj.FJ_xmax
public final class FJ_xmax extends Object

  • Nested Class Summary

    Nested Classes
    Modifier and Type
    Class
    Description
    static final class 
    FJ_xmax.FJXmaxNormalResult
    Result container for expected maximum of normal distribution.
    static final class 
    FJ_xmax.FJXmaxParetoResult
    Result container for expected maximum of Pareto distribution.

  • Method Summary

    Modifier and Type
    Method
    Description
    static double
    fj_harmonic(int K)
     
    static double
    fj_xmax_2(double lambda)
    Expected maximum of 2 i.i.d.
    static double
    fj_xmax_2(double lambda1, double lambda2)
    Expected maximum of 2 exponential random variables.
    static double
    fj_xmax_approx(int K, double muX, double sigmaX)
     
    static double
    fj_xmax_approx(int K, double muX, double sigmaX, String distType)
    General approximation for expected maximum of K random variables.
    static double
    fj_xmax_emma(int K, double mu)
    Expected maximum using EMMA.
    static double
    fj_xmax_emma(int K, DoubleUnaryOperator Finv)
    Expected maximum using EMMA for a general distribution given by its inverse CDF (quantile function): E[Y_K] = F^{-1}(phi^(1/K)) with phi = 0.570376 (the MATLAB 'general' branch of fj_xmax_emma).
    static double
    fj_xmax_erlang(int K, int k, double mu)
    Expected maximum of K i.i.d.
    static double
    fj_xmax_exp(int K, double mu)
    Expected maximum of K i.i.d.
    static double
    fj_xmax_hyperexp(int K, double p1, double mu1, double mu2)
    Expected maximum of K i.i.d.
    static FJ_xmax.FJXmaxNormalResult
    fj_xmax_normal(int K, double mu, double sigma)
     
    static FJ_xmax.FJXmaxNormalResult
    fj_xmax_normal(int K, double mu, double sigma, String method)
    Expected maximum for normal distribution.
    static double
    fj_xmax_pareto(int K, double beta)
     
    static double
    fj_xmax_pareto(int K, double beta, double k)
    Expected maximum for Pareto distribution.
    static double
    fj_xmax_pareto_char_max(int K, double beta, double k)
    Characteristic maximum M_K for Pareto distribution.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Method Details

    • fj_harmonic

      public static double fj_harmonic(int K)

    • fj_xmax_exp

      public static double fj_xmax_exp(int K, double mu)
      Expected maximum of K i.i.d. exponential random variables.

    • fj_xmax_2

      public static double fj_xmax_2(double lambda1, double lambda2)
      Expected maximum of 2 exponential random variables.

    • fj_xmax_2

      public static double fj_xmax_2(double lambda)
      Expected maximum of 2 i.i.d. exponential random variables (same rate).

    • fj_xmax_erlang

      public static double fj_xmax_erlang(int K, int k, double mu)
      Expected maximum of K i.i.d. Erlang-k random variables.

    • fj_xmax_hyperexp

      public static double fj_xmax_hyperexp(int K, double p1, double mu1, double mu2)
      Expected maximum of K i.i.d. Hyperexponential-2 random variables.

    • fj_xmax_normal

      public static FJ_xmax.FJXmaxNormalResult fj_xmax_normal(int K, double mu, double sigma, String method)
      Expected maximum for normal distribution.

    • fj_xmax_normal

      public static FJ_xmax.FJXmaxNormalResult fj_xmax_normal(int K, double mu, double sigma)

    • fj_xmax_pareto

      public static double fj_xmax_pareto(int K, double beta, double k)
      Expected maximum for Pareto distribution.

    • fj_xmax_pareto

      public static double fj_xmax_pareto(int K, double beta)

    • fj_xmax_pareto_char_max

      public static double fj_xmax_pareto_char_max(int K, double beta, double k)
      Characteristic maximum M_K for Pareto distribution.

    • fj_xmax_approx

      public static double fj_xmax_approx(int K, double muX, double sigmaX, String distType)
      General approximation for expected maximum of K random variables.

    • fj_xmax_approx

      public static double fj_xmax_approx(int K, double muX, double sigmaX)

    • fj_xmax_emma

      public static double fj_xmax_emma(int K, double mu)
      Expected maximum using EMMA.

    • fj_xmax_emma

      public static double fj_xmax_emma(int K, DoubleUnaryOperator Finv)
      Expected maximum using EMMA for a general distribution given by its inverse CDF (quantile function): E[Y_K] = F^{-1}(phi^(1/K)) with phi = 0.570376 (the MATLAB 'general' branch of fj_xmax_emma).
      Parameters:
      K - number of random variables (positive integer)
      Finv - inverse CDF function handle
      Returns:
      approximate expected maximum