Under what conditions would this occur? It seems to be nonsensical, from a mathematical perspective... what might it be doing from a Matlab perspective?
I'm fitting a million 4-d samples on a distribution with two "humps" that have a finite kurtosis so aren't quite gaussians but pretty close. with two or three component mixtures the results are pretty good and NlogL is positive. The third component just picks up some leftovers due to not quite gaussianity of my data. With 4 or more components, the results still look pretty good--two good components, the rest pick up leftovers. However, the NlogL (and BIC and AIC) are now negative... What am I to make of this?
In real data I won't know how many "humps" are in my data so I can't just set the number of components to two ahead of time.