A Family of Multivariate Abel series distributions of order k (original) (raw)

A Family of Multivariate Abel Series Distributions

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.

A FAMILY OF ABEL SERIES DISTRIBUTIONS OF ORDER k

2008

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.

Multivariate distributions of order k, part II

Statistics & Probability Letters, 1990

Several additional properties and genesis schemes of the multivariate distributions of order k of Philippou et al. (1989) are obtained. Some of them deal with two new distributions introduced presently, the multivariate k-point distribution and the modified multivariate logarithmic series distribution of order k.

A new generalization of logarithmic series distribution

Studia Scientiarum Mathematicarum Hungarica, Vol. 51(1), pp.41-49

A new generalization of the logarithmic series distribution has been obtained as a limiting case of the zero-truncated Mishra's (2011) generalized negative binomial distribution (GNBD). This distribution has an advantage over the Mishra's (2008) quasi logarithmic series distribution (QLSD) as its moments appear in compact forms unlike the QLSD, facilitating the estimation of its parameters. The first four moments of this distribution have been obtained and the distribution has been fitted to some well known data-sets to test its goodness of fit.

Multivariate distributions of order κ

Statistics & Probability Letters, 1988

Three mulUvariate dlstnbuttons of order k are introduced and studied. A multivariate negaUve blnormal dlstnbuuon of order k is derived first, by means of an urn scheme, and two hnutlng cases of it are obtained next. They are, respecuvely, a muluvanate Polsson dlstrtbutlon of order k and a multivariate loganthrmc series d~stnbut~on of the same order. The probab~hty generating functions, means variances and covanances of these distributions are obtamed, and some further genes~s schemes of them and mterrelat~onsbaps among them are also estabhshed. The present paper extends to the multivariate case the work of Phihppou (1987) on multlparameter distributions of order k. At the same ttme, several results of Akd on extended dlstnbutaons of order k are also generahzed to the multwanate case.

The Generalized Power Series Distributions And Their Application

Journal of Mathematics and Computer Science

Necessity of the use of more rich family discrete distributions is practically observable. In this paper, we study about new family of discrete distributions, as Inflated Parameter distributions. Then , we use the application of these distributions for data modeling of Insurance claims and indicate that these distributions have more appropriate approximation then corresponding distributions.

On Certain Conditions of Multivariate Power Series Distributions

International Journal of Open Problems in Computer Science and Mathematics, 2013

During the last decades, no researches have conducted in order to prove some properties of the of the multivariate power series distribution, as results of the present study proved that any multivariate power series distribution is determined uniquely from the mean-function of any marginal random variable. Furthermore these results indicated also that any given function satisfying certain conditions construct a random vector with multivariate power series distribution which has a mean of the marginal random variable. A useful technique can be applied in model building when we have information about the mean-function.

Multivariate distributions of order k on a generalized sequence

Statistics & Probability Letters, 1990

A generalized sequence of order k is defined first, as an extension of independent trials with multiple outcomes. Then, three multivariate distributions of order k, which are based on that sequence, are introduced and studied. The probability generating functions, means, variances and covariances of these distributions are obtained, and some interrelationships among them are also established. The present paper extends to the multivariate case the work of .

Notes on Generalized Half-Normal Power Series Distributions

In this paper we introduce the generalized half-normal power series (GHNPS) class of distributions which is obtained by compounding generalized half-normal (GHN) and power series distributions. We obtain some properties of the GHNPS distribution such as its probability density function, quantiles, moments, order statistics, mean residual life and reliability function. Sub-models of this family are studied in a real example.