Package jline.api.moment

Class Moment_central_from_raw

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

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

   m_n^c = sum_{k=0}^{n} (-1)^(n-k) * binom(n,k) * m_k * m_1^(n-k)

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_central_from_raw

      public static Matrix moment_central_from_raw(Matrix m)
      Converts power (raw) moments into central 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. At least the mean m_1 must be given, hence the length must be at least 2
      Returns:
      column vector of length n+1 holding m_0^c,...,m_n^c, with m_0^c = 1 and m_1^c = 0 by construction
      Throws:
      IllegalArgumentException - if m holds fewer than 2 elements