It is shown that the modified power series distribution (MPSD) [GUPTA, 1974] the Lagrange probability distribution (LPD) [CONSUL SHENTON, 1972, the LAGBANGE power series distribution (LPSD) [JAIN, 1975] and the discrete exponential family (DEE) distribution [JANARDAN, 1982) represent the same probability model. A theorem on the MVU estimation of a function (θ) of the parameter θ in the LPSD is stated with the necessary conditions. The theorem is then applied to derive the MVU estimators for the mean, square of the mean and the variance of the generalized POISSON .distribution, generalized negative binomial distribution and some other related distributions