A family of multivariate discrete distributions (original) (raw)
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Discrete multivariate distributions
2008
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson distributions. Accordingly to eventology new laws take into account full distribution of events. Also, in article its characteristics and properties are described
The Poisson-G Family of Distributions with Applications
Pakistan Journal of Statistics and Operation Research
We define and study a new class of continuous distributions called the Poisson-family. We present three of its several special models. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions and entropies are provided. The estimations of the model parameters is carried out using maximum likelihood method. The flexibility of the new family is illustrated by means of two applications to real data sets.
Finite mixtures of multivariate Poisson distributions with application
Journal of statistical planning and inference, 2007
In the present paper we examine finite mixtures of multivariate Poisson distributions as an alternative class of models for multivariate count data. The proposed models allow for both overdispersion in the marginal distributions and negative correlation, while they are computationally tractable using standard ideas from finite mixture modelling. An EM type algorithm for maximum likelihood (ML) estimation of the parameters is developed. The identifiability of this class of mixtures is proved. Properties of ML estimators are derived. A real data application concerning model based clustering for multivariate count data related to different types of crime is presented to illustrate the practical potential of the proposed class of models.
On a Generalised Exponential-Lindley Mixture of Generalised Poisson Distribution
Nepalese journal of statistics, 2020
Background: A mixture distribution arises when some or all parameters in a mixing distribution vary according to the nature of original distribution. A generalised exponential-Lindley distribution (GELD) was obtained by Mishra and Sah (2015). In this paper, generalized exponential-Lindley mixture of generalised Poisson distribution (GELMGPD) has been obtained by mixing generalised Poisson distribution (GPD) of Consul and Jain ' s (1973) with GELD. In the proposed distribution, GELD is the original distribution and GPD is a mixing distribution. Generalised exponential-Lindley mixture of Poisson distribution (GELMPD) was obtained by Sah and Mishra (2019). It is a particular case of GELMGPD. Materials and Methods: GELMGPD is a compound distribution obtained by using the theoretical concept of some continuous mixtures of generalised Poisson distribution of Consul and Jain (1973). In this mixing process, GELD plays a role of original distribution and GPD is considered as mixing distribution. Results: Probability mass of function (pmf) and the first four moments about origin of the generalised exponential-Lindley mixture of generalised Poisson distribution have been obtained. The method of moments has been discussed to estimate parameters of the GELMGPD. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature. P-value of this distribution has been compared to the PLD of Sankaran (1970) and GELMPD of Sah and Mishra (2019) for similar type of data-sets. Conclusion: It is found that P-value of GELMGPD is greater than that in each case of PLD and GELMPD. Hence, it is expected to be a better alternative to the PLD of Sankaran and GELMPD of Sah and Mishra for similar types of discrete data-sets which are negative binomial in nature. It is also observed that GELMGPD gives much more significant result when the value of is negative.
Characterisation of the multivariate negative binomial-generalised exponential distribution
2016
The negative binomial-generalised exponential distribution was recently developed. A multivariate negative binomial-generalised exponential (MNB-GE) distribution is consequently introduced and applied in a multivariate count data analysis. Some probabilistic properties of the proposed distribution are studied. A bivariate negative binomial-generalised exponential distribution is also shown as a special case of the MNB-GE distribution. Joint probability functions and characteristics of the proposed distributions are derived. We also consider both dependent and independent bivariate random variables. The maximum likelihood estimation technique is used to estimate the parameters of the proposed distributions. Furthermore, the application of accidents data is illustrated for both the univariate and bivariate versions.
This work is copyrighted byUniversi a del Salento, and is licensed un-der a Creative Commons Attribuzione -Non commerciale -Non opere derivate 3.0 Italia License. For more information see: In this paper, we have introduced a class of GPDs of order k upon using a class of Quasi Binomial distribution of order k and using Abels generalization of the Binomial formula from Riordan (1968). A few particular cases, like a class of GPD, GPD of order k and classical Poisson distribution have been studied. A mixture of Poisson and Generalized Poisson distribution along with their various inferential properties are discussed. Finally, the mixture of Poisson and GP distributions are fitted to some real life data and compared with classical Poisson distribution and GPD and the fittings of the mixture to the observed frequencies are found to be very good as judged by the corresponding chi-square values. keywords: Distributions of order k ; Mixtures of distributions; Generalized Poisson distributio...
Bayesian analysis of finite mixtures of multinomial and negative-multinomial distributions
Computational Statistics & Data Analysis, 2007
The Bayesian implementation of finite mixtures of distributions has been an area of considerable interest within the literature. Computational advances on approximation techniques such as Markov chain Monte Carlo (MCMC) methods have been a keystone to Bayesian analysis of mixture models. This paper deals with the Bayesian analysis of finite mixtures of two particular types of multidimensional distributions: the multinomial and the negative-multinomial ones. A unified framework addressing the main topics in a Bayesian analysis is developed for the case with a known number of component distributions. In particular, theoretical results and algorithms to solve the label-switching problem are provided. An illustrative example is presented to show that the proposed techniques are easily applied in practice.
A Generalization to the Family of Discrete Distributions
An alternative approaches for a couple of discrete distributions like Binomial and Multinomial, Poisson, etc having more general form of sampling method (more than one outcome in one trial) compared to tradition sampling heuristics have been suggested and termed as Generalized Binomial, Generalized Multinomial, Generalized Poisson, Generalized Geometric respectively. It is evident that the traditional existing distributions are the special cases of the proposed generalized distributions. The basic distributional properties of the proposed distributions have also been examined including the limiting form. Real life examples are cited for the respective distributions.
2014
This work is copyrighted by Università del Salento, and is licensed under a Creative Commons Attribuzione-Non commerciale-Non opere derivate 3.0 Italia License. For more information see: http://creativecommons.org/licenses/by-nc-nd/3.0/it/ In this paper, we have introduced a class of GPDs of order k upon using a class of Quasi Binomial distribution of order k and using Abels generalization of the Binomial formula from Riordan (1968). A few particular cases, like a class of GPD, GPD of order k and classical Poisson distribution have been studied. A mixture of Poisson and Generalized Poisson distribution along with their various inferential properties are discussed. Finally, the mixture of Poisson and GP distributions are fitted to some real life data and compared with classical Poisson distribution and GPD and the fittings of the mixture to the observed frequencies are found to be very good as judged by the corresponding chi-square values. keywords: Distributions of order k ; Mixture...