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.

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.

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 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 .

ON MULTIPARAMETER DISTRIBUTIONS OF ORDER k

Annals of the Institute of Statistical Mathematics, 1988

A multiparameter negative binomial distribution of order k is obtained by compounding the extended (or multiparameter) Poisson distribution of order k by the gamma distribution. A multiparameter logarithmic series distribution of order k is derived next, as the zero truncated limit of the first distribution. Finally a few genesis schemes and interrelationships are established for these three multiparameter distributions of order k. The present work extends several properties of distributions of order k. Key words and phrases: Multiparameter distributions of order k, type I and type II distributions of order k, genesis schemes and interrelationships, extended distributions of order k.

Multivariate Polya and Inverse Polya Distributions of Orderk

Biometrical Journal, 1991

Multivariate Polya and inverse Polya distributions of order k are derived by means of generalized urn models and by compounding the type I1 multinomial and multivariate negative binomial distributions of order k of PHLLEPPOU, ANTZOULAKOS and TICPSIANXIS (1990, 1988). respectively, with the Dirichlet distribution. It is noted that the above two distributions include as special cases a mu1tivariat.e hypergeometric distribution of order k, a negative one, an inverse one, a negative inverse one and a discrete uniform ofthe sameorder. Theprobabilitygenerating functions, means, variances and covariances of the new distributions are obtained and five asymptotic results are established relating them to the above-mentioned multinomial and multivariate negative binomial distributions 01 order k, and to the type I1 negative binomial and the type I multivariate Poisson distributions of order k Of PHILIPPOW (1983), and PHLLIpPOU, ANTZOULAKOS and TBIPSIANms (1988), respectively. Potential applications are also indicated. The present paper extends t o the multivariate case the work of P~P P O W , TBIPSIANNIS and k T Z 0~0 S (1989) on Polya and inverse Polya distributions of order k.