Package jline.api.moment

Class Moment_raw_from_central

java.lang.Object
jline.api.moment.Moment_raw_from_central
public final class Moment_raw_from_central extends Object
Power (raw) moments from central moments.

Converts the central moments m_n^c = E[(N-m_1)^n] of a random variable N into the power (raw) moments m_n = E[N^n] by means of the inverse binomial transform in the variation that involves the mean m_1, 

   m_n = sum_{k=0}^{n} binom(n,k) * m_k^c * m_1^(n-k)

The mean must be supplied separately since m_1^c = 0 carries no information on it. The conversion also holds for continuous random variables.

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_central

      public static Matrix moment_raw_from_central(Matrix mc, double m1)
      Converts central moments into power (raw) moments.
      Parameters:
      mc - column vector of length n+1 holding m_0^c,...,m_n^c, i.e. element i is the moment of order i and element 0 is m_0^c = 1
      m1 - mean of N
      Returns:
      column vector of length n+1 holding m_0,...,m_n