Package jline.api.moment

Class Moment_tail_from_binomial

java.lang.Object
jline.api.moment.Moment_tail_from_binomial
public final class Moment_tail_from_binomial extends Object
Survival (tail) probabilities from binomial moments. 
   t_m = sum_{j>=m} (-1)^(j-m) * nchoosek(j-1,m-1) * b_j,  m >= 1

with t_0 = 1. Inverse of Moment_binomial_from_tail. The inversion is exact on the finite box supplied, the matrix being unit upper triangular, but it reconstructs the true tail only if the binomial moments were themselves those of a law supported on 0,...,n.

Reference: A. Heindl and A. van de Liefvoort. Moment conversions for discrete distributions. PMCCS, 2003.

Since:
LINE 3.0

  • Method Details

    • moment_tail_from_binomial

      public static Matrix moment_tail_from_binomial(Matrix b)
      Converts binomial moments into survival probabilities.
      Parameters:
      b - column vector of length n+1 holding b_0,...,b_n
      Returns:
      column vector of length n+1 holding t_0,...,t_n