On the resolution of a mixture op observations from two modified power series distributions

The modified power series distributions (MPSD) introduced by Gupta (1974) includes a number of the well known discrete distributions. In this note we assume that a sample of N observations is available and that it consists of N₁ observations from a MPSD and N₂ observations from another MPSD. The maximum likelihood method is used to identify the population of origin of  each observation, and to estimate the mean and parameter of that population. Special cases are dealt with in detail. The variance of the estimate of N_i, i = 1,2, is derived.