Discrete distributions wherein the probabilities at different counts are affected in the sense "inflated" or "modified" are considered. The effect of modification and inflation on the variance is discussed. Generalized negative binomial is taken up as an example to illustrate this effect in the inflated case. Generalized poison is similarly considered for the modified case. Estimation of parameters as well as of modification and inflation rates is attempted by maximum likelihood (m.1.) approach. example. case. Actual estimates are obtained for a simple Bayes estimates are also suggested for the modified case.