Package jline.api.moment

Class Moment_factorial_from_raw

java.lang.Object
jline.api.moment.Moment_factorial_from_raw
public final class Moment_factorial_from_raw extends Object
Factorial moments from power (raw) moments.

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

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

Reference: A. Heindl and A. van de Liefvoort. Moment conversions for discrete distributions. PMCCS, 2003, eq. (13).

Since:
LINE 3.0

  • Method Details

    • moment_factorial_from_raw

      public static Matrix moment_factorial_from_raw(Matrix m)
      Converts power (raw) moments into 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