Article
A FAMILY OF ABEL SERIES DISTRIBUTIONS OF ORDER k
Pak. J. Statist. 2008 Vol. 24(3), 01/2008; 24:173178.
 Citations (17)
 Cited In (0)

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):557568. · 0.66 Impact Factor  [Show abstract] [Hide abstract]
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 negativebinomial data and provides with a model suitable to most unimodel or reverse Jshaped 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):791799. · 1.79 Impact Factor  [Show abstract] [Hide abstract]
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 quasilogarithmic series distribution is derived from ASD and many more wellknown distributions, viz., quasibinomial distribution, generalized Poisson distribution, quasinegative 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 quasibinomial 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; 56:147164.
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.