Package jline.api.moment

Class Moment_factorial_from_upfactorial

java.lang.Object
jline.api.moment.Moment_factorial_from_upfactorial
public final class Moment_factorial_from_upfactorial extends Object
Factorial moments from upward-factorial moments.

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

   f_n = sum_{k=1}^{n} (-1)^(n-k) * 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_factorial_from_upfactorial

      public static Matrix moment_factorial_from_upfactorial(Matrix fp)
      Converts upward-factorial moments into factorial moments.
      Parameters:
      fp - 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