  In finite mixtures of location-scale distributions, if there is no constraint
on the parameters then the maximum likelihood estimate does not exist. But when
the ratios of the scale parameters are restricted appropriately, the maximum
likelihood estimate exists. We prove that the maximum likelihood estimator
(MLE) is strongly consistent, if the ratios of the scale parameters are
restricted from below by $\exp(-n^{d}), 0 < d < 1 $, where $n$ is the sample
size.
