On Some New α-Modified Binomial and Poisson Distributions and Their Applications
A new class of α-modified binomial distribution has been proposed, and its distributional properties like probability generating function (pgf), moments, and their interrelations have been studied. Two new α-modified Poisson distributions and Poisson distribution have been obtained as limiting distributions. Modified binomial and Poisson distributions introduced by Berg and Jaworski (1988) have been seen as particular cases. Mixture distributions of α-modified binomial distributions have been derived. A new distributions called α-modified binomial distributions of type j, their moment properties, limiting distributions as α-modified Poisson distribution of type j, their different convolution properties, pgf, parameter estimators have been studied. Two more new distributions namely Doubly α-modified binomial distributions of type (i, j) and α-modified weighted generalized Poisson distributions of type (j − 1) have also been studied. Various α-modified binomial and Poisson distributions of Berg and Mutafchiev (1990) and Berg and Nowicki (1991) have been seen as special cases. Application of some of these proposed distributions have been identified.