overlap computes the exact overlap given the parameters of the mixture

`OmegaMap=overlap(k, v, Pi, Mu, S)`

example`OmegaMap=overlap(k, v, Pi, Mu, S, tol)`

example`OmegaMap=overlap(k, v, Pi, Mu, S, tol, lim)`

example`[OmegaMap, BarOmega]=overlap(___)`

example`[OmegaMap, BarOmega, MaxOmega]=overlap(___)`

example`[OmegaMap, BarOmega, MaxOmega, StdOmega]=overlap(___)`

example`[OmegaMap, BarOmega, MaxOmega, StdOmega, rcMax]=overlap(___)`

example

Maitra, R. and Melnykov, V. (2010), Simulating data to study performance of finite mixture modeling and clustering algorithms, "The Journal of Computational and Graphical Statistics", Vol. 19, pp. 354-376. [to refer to this publication we will use "MM2010 JCGS"]

Melnykov, V., Chen, W.-C. and Maitra, R. (2012), MixSim: An R Package for Simulating Data to Study Performance of Clustering Algorithms, "Journal of Statistical Software", Vol. 51, pp. 1-25.

Davies, R. (1980), The distribution of a linear combination of chi-square random variables, "Applied Statistics", Vol. 29, pp. 323-333.