Package jline.api.moment

Class Moment_raw_from_upfactorial

java.lang.Object
jline.api.moment.Moment_raw_from_upfactorial
public final class Moment_raw_from_upfactorial extends Object
Power (raw) 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 power (raw) moments m_n = E[N^n] by means of the signed Stirling numbers of the second kind, 

   m_n = sum_{k=0}^{n} (-1)^(n-k) * S(n,k) * f_k^+

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

Since:
LINE 3.0

  • Method Details

    • moment_raw_from_upfactorial

      public static Matrix moment_raw_from_upfactorial(Matrix fp)
      Converts upward-factorial moments into power (raw) 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 m_0,...,m_n