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.

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