Some Aspects of Discrete Probability Distributions of Order K

One of the important directions of research in the theory of discrete probability distribution is to develop/obtain a large class/family of probability distributions and investigate their various properties, problem of estimation, data fitting, etc. This book deals with the study of various distributions of order k, their distributional properties etc. to some new class of discrete probability distributions. An overview of discrete probability distributions of order k has been elaborated followed by the study of a class of Quasi Binomial distributions of order k, its probability function by considering Abel's generalization of the Binomial formula and some of their inferential properties have been discussed. Next, a family of univariate Abel series distributions of order k, some of their important properties have been found out. The multivariate case of the family of Abel series distributions of order k have been defined and discussed. Some of their inferential properties have been mentioned. Finally, zero-modified distributions of order k, such as Binomial distribution of order k, Poisson distribution of order k, etc. have been pointed out.