Package jline.api.moment

Class Moment_lah

java.lang.Object
jline.api.moment.Moment_lah
public final class Moment_lah extends Object
Triangle of the Lah numbers.

Builds the triangle of the Lah numbers L(i,j) = (i!/j!)*nchoosek(i-1,j-1), which link the factorial moments to the upward-factorial moments. The triangle is built from the equivalent recursion 

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

which avoids the overflow of the explicit factorial form for large orders.

References: A. Heindl and A. van de Liefvoort. Moment conversions for discrete distributions. PMCCS, 2003, Section 4. I. Lah. Eine neue Art von Zahlen, ihre Eigenschaften und Anwendung in der mathematischen Statistik. Mitteilungsbl. Math. Statist., 7:203-212, 1955.

Since:
LINE 3.0

  • Method Details

    • moment_lah

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