Package jline.api.moment

Class Moment_stirlingcycle

java.lang.Object
jline.api.moment.Moment_stirlingcycle
public final class Moment_stirlingcycle extends Object
Triangle of the Stirling cycle numbers.

Builds the triangle of the Stirling cycle numbers (unsigned Stirling numbers of the first kind), sigma(i,j) = (-1)^(i-j) * s(i,j), obtained from the recursion 

   sigma(i,j) = (i-1)*sigma(i-1,j) + sigma(i-1,j-1)   for j > 0
   sigma(0,0) = 1,   sigma(i,0) = 0 for i > 0

These numbers are the coefficients that convert power moments into upward-factorial moments.

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

Since:
LINE 3.0

  • Method Details

    • moment_stirlingcycle

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