Package jline.api.moment

Class Moment_binomial_from_negbinomial

java.lang.Object
jline.api.moment.Moment_binomial_from_negbinomial
public final class Moment_binomial_from_negbinomial extends Object
Binomial moments from negative-binomial moments.

Converts the negative-binomial moments b_n^- = E[binom(N+n-1,n)] of a discrete random variable N into the binomial moments b_n = E[binom(N,n)] by means of the shifted binomial transform 

   b_n = sum_{k=1}^{n} (-1)^(n-k) * binom(n-1,k-1) * b_k^-   for n >= 1
   b_0 = 1

Reference: A. Heindl and A. van de Liefvoort. Moment conversions for discrete distributions. PMCCS, 2003, eq. (14).

Since:
LINE 3.0

  • Method Details

    • moment_binomial_from_negbinomial

      public static Matrix moment_binomial_from_negbinomial(Matrix bm)
      Converts negative-binomial moments into binomial moments.
      Parameters:
      bm - column vector of length n+1 holding b_0^-,...,b_n^-, i.e. element i is the moment of order i and element 0 is b_0^- = 1
      Returns:
      column vector of length n+1 holding b_0,...,b_n