Constructor Detail

Method Detail

• fj_gk_bound

   final static Double fj_gk_bound(Integer K, String type)

  Compute G(K) factors for expected maximum approximation.

  G(K) is used in: X_K^max ~ mu_X + sigma_X * G(K)

  Available formulas:

  • Exponential: G(K) = H_K - 1

  • Uniform: G(K) = sqrt(3) * (K-1) / (K+1)

  • EVD: G(K) = sqrt(6) * ln(K) / pi

  • Upper bound: G(K) <= (K-1) / sqrt(2K-1)

  Parameters:

  K - Number of random variables (positive integer)

  type - "exp", "uniform", "evd", "bound", or "all" (default)

  Returns:

  G(K) value for specified type, or -1 if "all" (use fj_gk_bound_all)

• fj_gk_bound_all

   final static GKBoundResult fj_gk_bound_all(Integer K)

  Compute all G(K) bound factors.

  Parameters:

  K - Number of random variables (positive integer)

  Returns:

  GKBoundResult with all G(K) values

• fj_order_stat_cdf

   final static Double fj_order_stat_cdf(Double FXy, Integer k, Integer K)

  CDF of k-th order statistic of K i.i.d. random variables.

  For maximum (k=K): F_{Y_K}(y) = F_X(y)^K

  For k-th order statistic (k-th smallest): F_{Y_k}(y) = sum_{j=k}^{K} C(K,j) * F_X(y)^j * (1-F_X(y))^{K-j}

  Parameters:

  FXy - CDF value F_X(y) at point y

  k - Order of the statistic (1 = minimum, K = maximum)

  K - Total number of random variables

  Returns:

  CDF of k-th order statistic F_{Y_k}(y)

• fj_order_stat_expected_max

   final static Double fj_order_stat_expected_max(Integer K, Function1<Double, Double> cdfFunc, Double upperLimit)

  Expected value of the maximum of K i.i.d. random variables via numerical integration.

  EY_K = integral_0^inf 1 - F_X(y)^K dy

  Parameters:

  K - Total number of random variables

  cdfFunc - CDF function F_X(y) -- a lambda/function that takes a Double and returns Double

  upperLimit - Upper integration limit (where CDF is very close to 1)

  Returns:

  Expected value EY_K

• fj_order_stat_expected_min

   final static Double fj_order_stat_expected_min(Integer K, Function1<Double, Double> cdfFunc, Double upperLimit)

  Expected value of the minimum of K i.i.d. random variables via numerical integration.

  EY_1 = integral_0^inf 1 - F_X(y)^K dy

  Parameters:

  K - Total number of random variables

  cdfFunc - CDF function F_X(y)

  upperLimit - Upper integration limit

  Returns:

  Expected value EY_1