Package jline.api.moment

Class Moment_joint_factcumulant_from_factorial

java.lang.Object
jline.api.moment.Moment_joint_factcumulant_from_factorial
public final class Moment_joint_factcumulant_from_factorial extends Object
Joint factorial cumulants from joint factorial moments.

The joint factorial cumulants are the coefficients of the logarithm of the joint probability generating function expanded about z = (1,...,1), 

   log E[prod_j z_j^(N_j)] = sum_(a != 0) kappa_a prod_j (z_j-1)^(a_j) / a_j!

and stand to the joint factorial moments exactly as the joint cumulants stand to the joint power moments, so the same recursion applies. For a multivariate Poisson vector with independent components every joint factorial cumulant of order two or more vanishes; for the per-class counts of a marked MAP they measure the departure from independent Poisson marking.

Reference: V. P. Leonov and A. N. Shiryaev. On a method of calculation of semi-invariants. Theory of Probability and its Applications, 4(3):319-329, 1959.

Since:
LINE 3.0

  • Method Details

    • moment_joint_factcumulant_from_factorial

      public static double[] moment_joint_factcumulant_from_factorial(double[] f, int[] dims)
      Converts joint factorial moments into joint factorial cumulants.
      Parameters:
      f - flattened joint factorial moments in row-major order, element 0 being 1
      dims - extents of the array, dims[j] = n_j+1
      Returns:
      flattened joint factorial cumulants, same layout