Package jline.api.moment

Class Moment_upfactorial_from_raw

java.lang.Object
jline.api.moment.Moment_upfactorial_from_raw
public final class Moment_upfactorial_from_raw extends Object
Upward-factorial moments from power (raw) moments.

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

   f_n^+ = sum_{k=0}^{n} sigma(n,k) * m_k

Upward-factorial moments are of use in moment-matching techniques for matrix-geometric and discrete phase-type distributions.

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_raw

      public static Matrix moment_upfactorial_from_raw(Matrix m)
      Converts power (raw) moments into upward-factorial moments.
      Parameters:
      m - column vector of length n+1 holding m_0,...,m_n, i.e. element i is the moment of order i and element 0 is m_0 = 1
      Returns:
      column vector of length n+1 holding f_0^+,...,f_n^+