Some Aspects of Zero modified distributions of order k

Under certain simplifying assumptions, zero-modified distribution of order k has been introduced and defined. In this paper, an attempt is made to study different zero-modified distributions of order k such as Binomial, Poisson, Geometric, Negative Binomial and logarithmic series. Also an inflated generalized Poisson distribution of order k has been defined and studied. Some of their properties also have been discussed.