Rankcluster (version 0.93.1)

kullback: Kullback-Leibler divergence

Description

This function computes the Kullback-Leibler divergence between two mixtures of multidimensional ISR distributions.

Usage

kullback(proportion1, pi1, mu1, proportion2, pi2, mu2, m)

Arguments

proportion1, proportion2

vectors (which sums to 1) containing the K mixture proportions.

pi1, pi2

matrices of size K*p, where K is the number of clusters and p the number of dimension, containing the probabilities of a good comparaison of the model (dispersion parameters).

mu1, mu2

matrices of size K*sum(m), containing the modal ranks. Each row contains the modal rank for a cluster. In the case of multivariate ranks, the reference rank for each dimension are set successively on the same row.

m

a vector containing the size of ranks for each dimension.

Value

a real, the Kullback-Leibler divergence.

References

http://en.wikipedia.org/wiki/Kullback

Examples

proportion1=c(0.4,0.6)
pi1=matrix(c(0.8,0.75),nrow=2)
mu1=matrix(c(1,2,3,4,4,2,1,3),nrow=2,byrow=TRUE)
proportion2=c(0.43,0.57)
pi2=matrix(c(0.82,0.7),nrow=2)
mu2=matrix(c(1,2,3,4,4,2,1,3),nrow=2,byrow=TRUE)
dK=kullback(proportion1,pi1,mu1,proportion2,pi2,mu2,4)