Package jline.api.fj

Class FJ_order_stat

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

  • Method Details

    • fj_gk_bound

      public static double fj_gk_bound(int K, String type)
      Compute G(K) factors for expected maximum approximation.

    • fj_gk_bound

      public static double fj_gk_bound(int K)

    • fj_gk_bound_all

      public static GKBoundResult fj_gk_bound_all(int K)
      Compute all G(K) bound factors.

    • fj_order_stat

      public static OrderStatResult fj_order_stat(double y, int k, int K, DoubleUnaryOperator F_X)
      CDF of the k-th order statistic (k-th smallest) of K i.i.d. random variables at y, together with its expected value (port of MATLAB fj_order_stat with two outputs).

      F_{Y_k}(y) = sum_{j=k}^{K} C(K,j) F_X(y)^j (1-F_X(y))^{K-j} (F_X(y)^K for k=K). The mean is E[Y_K] = integral_0^inf [1-F_X^K] for the maximum, E[Y_1] = integral_0^inf [1-F_X]^K for the minimum and, for 1<k<K, integral_0^inf t K C(K-1,k-1) f_X(t) F_X(t)^{k-1} (1-F_X(t))^{K-k} dt with the central finite-difference density f_X (eps=1e-8). The horizon is the first u=2^n with F_X(u) >= 0.999999.

      Parameters:
      y - value at which the CDF is evaluated
      k - order of the statistic (1 = minimum, K = maximum)
      K - total number of random variables
      F_X - CDF function handle
      Returns:
      [F_Yk, E_Yk]

    • fj_order_stat_cdf

      public static double fj_order_stat_cdf(double FXy, int k, int K)
      CDF of k-th order statistic of K i.i.d. random variables.

    • fj_order_stat_expected_max

      public static double fj_order_stat_expected_max(int K, DoubleUnaryOperator cdfFunc, double upperLimit)
      Expected value of the maximum of K i.i.d. random variables via numerical integration.

    • fj_order_stat_expected_min

      public static double fj_order_stat_expected_min(int K, DoubleUnaryOperator cdfFunc, double upperLimit)
      Expected value of the minimum of K i.i.d. random variables via numerical integration.