Power series distribution sand zero-inflated models

There are two main objectives in this project. First, to construct Power Series Distributions and obtain their properties. Specically, to express the Power Series Distributions in explicit form, in recursive form (in Katz recursive form), special function form (in terms of Confluent and Gauss hypergeometric functions), expectation form (in terms of probability generating functions) Secondly, to generalize Power Series Distributions by introducing an inflated parameter. Specifically, (i) To construct an inflated Poisson, Binomial, Negative Binomial and Logarithmic distributions. (ii) To obtain the moments and the maximum likelihood estimators of the zero inflated power series distributions. (iii) To obtain Compound Poisson distributions for the inflated power series distributions. (iv) Application of the inflated models described above to migration data