Package jline.api.moment

Class Moment_joint_aggregate

java.lang.Object
jline.api.moment.Moment_joint_aggregate
public final class Moment_joint_aggregate extends Object
Factorial moments of a total count from the joint factorial moments of its parts.

For N = N_1+...+N_d the Vandermonde convolution of falling factorials gives 

   f_n = sum_(|a|=n) (n! / prod_j a_j!) * F_a

which holds for ANY joint law of the parts, marked or not, and is the inverse direction of Moment_joint_marking whenever the marking is multinomial. The order reached is limited by the smallest per-class order in F, since the term a = n*e_j must be available for every j.

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

Since:
LINE 3.0

  • Method Details

    • moment_joint_aggregate

      public static Matrix moment_joint_aggregate(double[] F, int[] dims)
      Factorial moments of the total count.
      Parameters:
      F - flattened joint factorial moments of the parts, row-major order
      dims - extents of the array, dims[j] = n_j+1
      Returns:
      column vector of length min_j(n_j)+1 holding the factorial moments of the total