Multivariate distributions of order k, part II (original) (raw)

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 Family of Multivariate Abel Series Distributions of Order k

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.

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.

A Family of Multivariate Abel Series Distributions

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 SOME NEW CLASSES OF MULTIVARIATE PROBABILITY DISTRIBUTIONS

New Classes of transformations on the Euclidean n-space R n are applied to sets of n (n = 2, 3, …) independent random variables T 1 , …, T n. Basically two cases are considered: 1) the random variables are all Weibullian, and 2) they are all gamma. The transformations, when applied to the random vectors (T 1 , …, T n), produce, as outputs, r. vectors (X 1 , …, X n) whose joint probability densities are investigated. The new probability densities of (X 1 , …, X n) produced by the Weibullian input r. variables T 1 , …, T n are called " pseudoWeibullians " , and the other " pseudogammas ". The origin and the basis for new methods of pdfs construction is set of problems associated with multicomponent system reliability modeling. In this context the random variables X 1 , …, X n are used to represent the system components life times.

A multivariate generalization of the power exponential family of distributions

Communications in Statistics-theory and Methods, 1998

This paper proposes a multivariate generalization of the power exponential distribution family. It will be useful in modelizing random phenomena and it will robustify many statistical procedures. Its definition and main properties are given. A procedure to simulate observations from this distribution is derived. Finally, an example adjusted to a bidimensional power exponential distribution is shown. Ã Σ 11 0 p×(n−p) 0 (n−p)×p Σ 22.1 ! and the same β parameter as X.

A family of multivariate discrete distributions

South African Statistical Journal, 2020

In this short paper, the multivariate Poisson-Gamma, the multinomial N-mixture and the negative multinomial distributions are shown to have probability mass functions of the same form and thus to share, broadly, the same distributional properties. The three distributions are, however, fundamentally very different in nature, that is, in terms of genesis, interpretation and model building, and these differences are highlighted and discussed.

General results for the Marshall and Olkin's family of distributions

Anais da Academia Brasileira de Ciências, 2013

Marshall and Olkin (1997) introduced an interesting method of adding a parameter to a well-established distribution. However, they did not investigate general mathematical properties of their family of distributions. We provide for this family of distributions general expansions for the density function, explicit expressions for the moments and moments of the order statistics. Several especial models are investigated. We discuss estimation of the model parameters. An application to a real data set is presented for illustrative purposes.

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 (original) (raw)

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