Package jline.api.moment

Class Moment_binotrans

java.lang.Object
jline.api.moment.Moment_binotrans
public final class Moment_binotrans extends Object
Binomial transform of a sequence.

Computes the binomial transform of the sequence x_0,x_1,...,x_n into y_0,y_1,...,y_n, 

   y_n = sum_{k=0}^{n} (-1)^(n-k) * nchoosek(n,k) * x_k

Applied to a moment sequence m_i = E[X^i] it returns the moments of the unit downshift, y_i = E[(X-1)^i]. It is not an involution: its inverse is Moment_binotransinv, the unsigned transform.

Reference: A. Heindl and A. van de Liefvoort. Moment conversions for discrete distributions. PMCCS, 2003, eq. (8).

Since:
LINE 3.0

  • Method Details

    • moment_binotrans

      public static Matrix moment_binotrans(Matrix x)
      Binomial transform of a sequence.
      Parameters:
      x - column vector of length n+1 holding x_0,...,x_n, i.e. element i is the element of order i
      Returns:
      column vector of length n+1 holding y_0,...,y_n