**Sankhya: The Indian Journal of Statistics**

1996, Volume 58, Series A, Pt. 2, pp. 252--263

**A FAMILY OF THE MULTIVARIATE ABEL SERIES DISTRIBUTIONS**

By

S. B. NANDI, *Gauhati University*

and

K. K. DAS,* Karimganj College*

SUMMARY. In this paper the multivariate Abel series distributions (MASDs) are defined. From MASDs a new distribution, called the quasi multivariate logarithmic series distribution(QMLSD) is derived. Some well known distribution (QMLSD) is derived. Some well known distributions are also obtained by a new method of derivation. Some properties of quasi negative multinomial distribution (QNMD) are studied. A few examples of MASDs are cited from some real life situations. Further we develop acyclic quasi multinomial distributions (AQMDs). Finally, some special cases of AQMDs are considered.

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

*Key words and phrases.* Multivariate Abel series distribution, multivariate quasi logarithmic series distribution, quasi negative multinomial distribution, acyclic quasi multinominal distribution, Boolean multinomial Abel polynomial.