Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 2 , pp. 147--164

A FAMILY OF THE ABEL SERIES DISTRIBUTIONS

By

S. B. NANDI, *Gauhati University*

and

K. K. DAS, *Karimganj College*

SUMMARY. In this paper we consider a class of univariate discrete distributions, the Abel series distributions (ASDs) generated by suitable functions of real valued parameters in the Abel polynomials. A new distribution called the quasi-logarithmic series distribution. (QLSD) is derived from ASD and many more well known distributions, viz., quasi-binomial distribution (QNBD) etc., are also obtained from ASD. Some properties of the distributions are discussed. Generalised binomial numbers and their properties are studied. Moreover, we define generalised quasifactorial series distribution (GQFSD). We find some particular cases of GQFSD. Further, we derive acyclic quasi-binomial distributions (AQBDs). A few cases of AQBDs are considered. Finally, we fit a number of distributions to life data and test the goodness of fit of these distributions.

*AMS (1980) subject classification.* 62E15,62F10, 60E05, 62P10, 62P25.

*Key words and phrases.* Abel series distribution, quasibinomial distribution, quasinegative binomial distribution, quasi-logarithmic series distribution, generalized Poisson distribution, generalized binomial number, generalized quasi-factorial series distribution, acyclic quasi-binomial distribution.