Package jline.api.moment

Class Moment_stirling1

java.lang.Object
jline.api.moment.Moment_stirling1
public final class Moment_stirling1 extends Object
Triangle of the signed Stirling numbers of the first kind.

Builds the triangle of the signed Stirling numbers of the first kind s(i,j), defined as the coefficients of x^j in the falling factorial 

   sum_{j=0}^{i} s(i,j) x^j = x(x-1)(x-2)...(x-i+1)

These numbers are the coefficients that convert power moments into factorial moments. They relate to the Stirling cycle numbers via s(i,j) = (-1)^(i-j) * sigma(i,j).

Reference: A. Heindl and A. van de Liefvoort. Moment conversions for discrete distributions. PMCCS, 2003, eq. (10) and eq. (12).

Since:
LINE 3.0

  • Method Details

    • moment_stirling1

      public static Matrix moment_stirling1(int n)
      Triangle of the signed Stirling numbers of the first kind s(i,j).
      Parameters:
      n - maximum order (n >= 0)
      Returns:
      (n+1)x(n+1) matrix with element (i,j) holding s(i,j) in the 0-based notation of the reference; entries with j > i are zero
      Throws:
      IllegalArgumentException - if n is negative