Package jline.api.moment

Class Moment_raw_from_factorial

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

   m_n = sum_{k=0}^{n} S(n,k) * f_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_raw_from_factorial

      public static Matrix moment_raw_from_factorial(Matrix f)
      Converts factorial moments into power (raw) 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 m_0,...,m_n