On Some New α-Modified Binomial and Poisson Distributions and Their Applications
Subrata Chakraborty · Communication in Statistics- Theory and Methods · 2008
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 Berg , S. , Jaworski , J. ( 1988 ). Modified binomial and Poisson distributions with application in random mapping theory . J. Statist. Plann. Infer. 18 : 313 – 322 . [Google Scholar]) 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 Berg , S. , Mutafchiev , L. ( 1990 ). Random mapping with an attracting center: Lagrangian distributions and a regression function . J. Appl. Probab. 27 : 622 – 636 . [Google Scholar]) and Berg and Nowicki (1991 Berg , S. , Nowicki , K. ( 1991 ). Statistical inference for a class of modified power series distributions with applications to random mapping theory . J. Statist. Plann. Infer. 28 : 247 – 261 . [Google Scholar]) have been seen as special cases. Application of some of these proposed distributions have been identified.