A Generalized Poisson Distribution

Chandra, Nimai Kumar; Roy, Dilip; Ghosh, Tirthankar

doi:10.1080/03610926.2011.620207

Cited by 12 publications

(6 citation statements)

References 12 publications

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“…Suppose we have N documents that assumed Poisson distribution with rate , the probability mass function of having n realizations of N is given by [15]:…”

Section: Generalized Poisson Distributionmentioning

confidence: 99%

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GPLDA: A Generalized Poisson Latent Dirichlet Topic Model

Bala¹,

Saringat²

2019

IJACSA

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The earliest modification of Latent Dirichlet Allocation (LDA) in terms of words or document attributes is by relaxing its exchangeability assumption via the Bag-of-word (BoW) matrix. Several authors have proposed many modifications of the original LDA by focusing on model that assumes the current topic depends on the words from previous topic. Most of the earlier work ignored the document length distribution since it is assumed that it will fizzle out at the modelling stage. Thus, in this paper, the Poisson document length distribution of LDA model is replaced with Generalized Poisson (GP) distribution which has the strength of capturing complex structures. The main strengths of GP are in capturing overdispersed (variance larger than mean) and under dispersed (variance smaller than mean) count data. The Poisson distribution used by LDA strongly relies on the assumption that the mean and variance of document lengths are equal. This assumption is often unrealistic with most real-life text data where the variance of document length may be greater than or less than their mean. Approximate estimate of the GPLDA model parameters was achieved using Newton-Raphson approximation technique of log-likelihood. Performance and comparative analysis of GPLDA with LDA using accuracy and F 1 showed improved results.

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“…Suppose we have N documents that assumed Poisson distribution with rate , the probability mass function of having n realizations of N is given by [15]:…”

Section: Generalized Poisson Distributionmentioning

confidence: 99%

“…The Generalized Poisson (GP) [15][16][17][18] which is the extension of (1) can be defined in terms of additional dispersion parameter as:…”

Section: Generalized Poisson Distributionmentioning

confidence: 99%

GPLDA: A Generalized Poisson Latent Dirichlet Topic Model

Bala¹,

Saringat²

2019

IJACSA

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“…Consider the GP distribution (Chandra, Roy, & Ghosh, 2013;Consul & Jain, 1973;Hubert, Lauretto, & Stern, 2009;Lerner, Lone, & Rao, 1997;Srivastava & Chen, 2010;Tuenter, 2006) (following the notation of Consul & Jain, 1973) of a random variable X with the following probability function…”

Section: Generalised Poisson Difference Distributionmentioning

confidence: 99%

Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

Shahtahmassebi¹,

Moyeed²

2014

IJSP

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Integer-valued random variables arising from the difference of two discrete variables can be seen frequently in various applications. In this paper, we obtain the distribution and derive the properties of the difference of two generalised Poisson variables with unequal parameters. This distribution is adopted to model a set of ultra high frequency (UHF) data relating to FTSE100 index futures using covariates. The unique characteristics of UHF data have introduced new theoretical and computational challenges to both statistical and financial studies. Such data consist of discrete-valued observations and unequally spaced time intervals. We also extend the model to its zero inflated version in order to capture the excess of zeros in the given data set. The analysis is carried out in a Bayesian framework using Markov Chain Monte Carlo methods. Various model diagnostics and model comparisons were undertaken which showed that index changes were explained well by the fitted model.

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“…the variable of interest is a count variable. Though classical models like Poisson, geometric, negative binomial, and their generalizations (see for example Philippou (1983), Gómez (2010, Chandra et al (2013), Sastry et.al. (2014)), are available for count data analysis, it is found that these models are not supportive to capture the right tail behaviour of the data set properly.…”

Section: Introductionmentioning

confidence: 99%

A New Generalized Poisson-Lindley Distribution: Applications and Properties

Bhati

Sastry

Qadri³

2015

AJS

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A new generalized Poisson-Lindley distribution is obtained by compounding Poisson distribution with a two parameter generalised Lindley distribution. The new distribution is shown to be unimodal and over-dispersed. This distribution has a tendency to accommodate right tail, and for particular values of parameter, the tail tends to zero at a faster rate. Various properties like cumulative distribution function, generating function, moments etc. are derived. Knowledge about the parameters is obtained through method of moments, maximum likelihood method and EM algorithm. Moreover, an actuarial application to collective risk model is shown by considering the proposed distribution as primary distribution and exponential and Erlang as secondary distributions. The model is applied to real data sets and found to perform better than other competing models.

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A Generalized Poisson Distribution

Cited by 12 publications

References 12 publications

GPLDA: A Generalized Poisson Latent Dirichlet Topic Model

GPLDA: A Generalized Poisson Latent Dirichlet Topic Model

Bayesian Modelling of Integer Data Using the Generalised Poisson Difference Distribution

A New Generalized Poisson-Lindley Distribution: Applications and Properties

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