Maximum likelihood estimator in the case of simplest grouping of data

Maximum likelihood estimators from $k$ samples are considered for the location parameter $\nu$ and the scale parameter $\sigma$, each of the samples being grouped in a simplest way. For the class of distribution functions under consideration, the necessary and sufficient conditions for the existence and uniqueness of the maximum likelihood equations' solution are derived. It is proved also that this solution is the absolute maximum of the maximum likelihood function.