Package jline.api.moment

Class Moment_joint_marking

java.lang.Object

jline.api.moment.Moment_joint_marking

public final class Moment_joint_marking
extends Object

Joint factorial moments of the per-class counts under multinomial marking.

If a count N is marked independently, every event receiving class j with probability p_j, then the per-class counts (N_1,...,N_d) have joint factorial moments

   E[prod_j (N_j)_(a_j)] = (prod_j p_j^(a_j)) * f_(|a|)
 

where f is the factorial moment sequence of the aggregate count N and |a| = a_1+...+a_d. This is the counting-process counterpart of the marking (class-splitting) formulas of the M3A fitters, and it is exact for the per-class counts of a MAP marked in this i.i.d. way, in particular for an MMAP whose marking probabilities do not depend on the phase.

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

Since:

LINE 3.0

Method Summary

Modifier and Type	Method	Description
static double[]	moment_joint_marking(Matrix f, double[] p, int[] dims)	Joint factorial moments of the per-class counts.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

moment_joint_marking

public static double[] moment_joint_marking(Matrix f,
 double[] p,
 int[] dims)

Joint factorial moments of the per-class counts.

Parameters:

f - column vector of length n+1 holding the factorial moments of the aggregate count

p - marking probabilities, one per class

dims - maximum order per class; their sum must not exceed n

Returns:

flattened joint factorial moments in row-major order, of extent (dims[0]+1)*...*(dims[d-1]+1)