A FAMILY OF ABEL SERIES DISTRIBUTIONS OF ORDER k
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.
SourceAvailable from: Charalambos A. Charalambides
Article: On discrete distributions of order k[Show abstract] [Hide abstract]
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.Annals of the Institute of Statistical Mathematics 11/1986; 38(1):557-568. DOI:10.1007/BF02482543 · 0.66 Impact Factor
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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.Technometrics 11/1973; 15(4):791-799. DOI:10.1080/00401706.1973.10489112 · 1.79 Impact Factor
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ABSTRACT: 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 is derived from ASD and many more well-known distributions, viz., quasi-binomial distribution, generalized Poisson distribution, quasi-negative binomial distribution etc., are also obtained from ASD. Some properties of the distributions are discussed. Generalized binomial numbers and their properties are studied. Moreover, we define generalized quasifactorial series distribution (GQFSD). We find some particular cases of GQFSD. Further, we derive acyclic quasi-binomial distributions (AQBDs). A few special cases of AQBDs are considered. Finally, we fit a number of distributions to life data and test the goodness of fit of these distributions.Sankhya 01/1994; 56:147-164.