Pak. J. Statist. 2008 Vol. 24(3), 01/2008; 24:173-178.

ABSTRACT In this paper we have considered a class of univariate discrete distributions of order k,
the Abel Series Distributions of order k (ASD(k)) generated by suitable functions of real
valued parameters in the Abel polynomials. A new distribution called the Quasi
Logarithmic Series Distribution of order k (QLSD(k)) is derived from ASD(k) and many
other distributions, viz. Quasi Binomial distributions of order k (QBD(k)), Generalized
Poison distribution of order k (GPD(k)) and Quasi negative binomial distribution of order
k (QNBD (k)) have been derived as particular cases of ASDs of order k. Some properties
have also been discussed.

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    ABSTRACT: The class of discrete distributions of orderk is defined as the class of the generalized discrete distributions with generalizer a discrete distribution truncated at zero and from the right away fromk+1. The probability function and factorial moments of these distributions are expressed in terms of the (right) truncated Bell (partition) polynomials and several special cases are briefly examined. Finally a Poisson process of orderk, leading in particular to the Poisson distribution of orderk, is discussed.
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    ABSTRACT: A new generalization of the Poisson distribution, with two parameters λ1 and λ2, is obtained as a limiting form of the generalized negative binomial distribution. The variance of the distribution is greater than, equal to or smaller than the mean according as λ2 is positive, zero or negative. The distribution gives a very close fit to supposedly binomial, Poisson and negative-binomial data and provides with a model suitable to most unimodel or reverse J-shaped distributions. Diagrams showing the variations in the form of the distribution for different values of λ1 and λ2 are given.
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    ABSTRACT: In this paper an attempt is made to define the multivariate abel series distributions (MASDs) of order k. From MASD of order k, a new distribution called the quasi multivariate logarithmic series distribution (QMLSD) of order k is derived. Some well known distributions are also obtained by a new method of derivation. Limiting distribution of QNMD of order k are studied.
    Applied Mathematical Sciences. 01/2008; Vol. 2:2239 - 2246.

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