Package jline.api.moment

Class Moment_upfactorial_from_factorial

java.lang.Object
jline.api.moment.Moment_upfactorial_from_factorial
public final class Moment_upfactorial_from_factorial extends Object
Upward-factorial moments from factorial moments.

Converts the factorial moments f_n = E[N(N-1)...(N-n+1)] of a discrete random variable N into the upward-factorial moments f_n^+ = E[N(N+1)...(N+n-1)] by means of the Lah numbers, 

   f_n^+ = sum_{k=1}^{n} L(n,k) * f_k   for n >= 1
   f_0^+ = 1

Reference: A. Heindl and A. van de Liefvoort. Moment conversions for discrete distributions. PMCCS, 2003, Section 4.

Since:
LINE 3.0

  • Method Details

    • moment_upfactorial_from_factorial

      public static Matrix moment_upfactorial_from_factorial(Matrix f)
      Converts factorial moments into upward-factorial moments.
      Parameters:
      f - column vector of length n+1 holding f_0,...,f_n, i.e. element i is the moment of order i and element 0 is f_0 = 1
      Returns:
      column vector of length n+1 holding f_0^+,...,f_n^+