Package jline.api.moment

Class Moment_raw_from_cumulant

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

Runs the exponential-formula recursion forward, 

   m_n = sum_{k=1}^{n} nchoosek(n-1,k-1) * kappa_k * m_(n-k)

with m_0 = 1. Inverse of Moment_cumulant_from_raw.

Reference: V. P. Leonov and A. N. Shiryaev. On a method of calculation of semi-invariants. Theory of Probability and its Applications, 4(3):319-329, 1959.

Since:
LINE 3.0

  • Method Details

    • moment_raw_from_cumulant

      public static Matrix moment_raw_from_cumulant(Matrix kappa)
      Converts cumulants into power (raw) moments.
      Parameters:
      kappa - column vector of length n+1 holding kappa_0,...,kappa_n; element 0 is ignored
      Returns:
      column vector of length n+1 holding m_0,...,m_n, with m_0 = 1