Package jline.api.moment

Class Moment_negbinomial_from_binomial

java.lang.Object
jline.api.moment.Moment_negbinomial_from_binomial
public final class Moment_negbinomial_from_binomial extends Object
Negative-binomial moments from binomial moments.

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

   b_n^- = sum_{k=1}^{n} 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_negbinomial_from_binomial

      public static Matrix moment_negbinomial_from_binomial(Matrix b)
      Converts binomial moments into negative-binomial moments.
      Parameters:
      b - 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^-