On Identifying the Population of Origin of Each Observation in a Mixture of Observations from Two Normal Populations

The gamma distribution, known also as the Erlangian distribution, and its special case the exponential distribution arise in many technological applications of statistics. The present note is on the problem of identifying the population of origin of each observation in a sample thought to be the result of mixing a random sample of size N 1, from a gamma distribution with scale parameter σ1 and an independent random sample of size N 2 from another gamma distribution with scale parameter σ2. We shall also be interested in the estimation of σ1 and σ2. The method of moments and the maximum likelihood method are applied to the solution of these problems.