The covariance structure of the bivariate weighted Poisson distribution and application to the Aleurodicus data

Nganga, P. C. Batsindila; Bidounga, Rufin; Mizère, Dominique

doi:10.16929/as/2019.1999.146

Cited by 3 publications

(5 citation statements)

References 7 publications

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“…A simple application of proposition 1 from the work of Batsindila et al(2019), gives us the following results…”

Section: Characteristicsmentioning

confidence: 91%

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The New Bivariate Conway-Maxwell-Poisson Distribution Obtained by the Crossing Method

Bidounga¹,

Maloumbi²,

Kitoti³

et al. 2020

IJSP

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Kimberly et al. had proposed in 2016 a bivariate function as a bivariate Conway-Maxwell-Poisson distribution (COM-Poisson) using the generalized bivariate Poisson distribution and the probability generating functions of the follow distributions: bivariate bernoulli, bivariate Poisson, bivariate geometric and bivariate binomial. By examining this paper we have shown that this bivariate function is constant and it double series is divergent, when it should have been 1. To overcome this deadlock, we propose a new bivariate Conway-Maxwell-Poisson distribution which is definetely a probability distribution based on the crossing method, method highlighted by Elion et al. in 2016 and revisited by Batsindila et al. and Mandangui et al. in 2019. And this is the purpose of this paper. To this bivariate distribution is attached two generalized linear models (GLM) whose resolution allows us to highlight, not only the independence between the variables forming the couple, but also the effect of the factors (or predictors) on these variables. The resulting correlation is negative, zero or positive depending on the values of a parameter; in particular for the bivariate Poisson distribution according to Berkhout and Plug. A simulation of data will be given at the end of the article to illustrate the model.

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“…A simple application of proposition 1 from the work of Batsindila et al(2019), gives us the following results…”

Section: Characteristicsmentioning

confidence: 91%

“…The couple (X, Y) follows the bivariate COM-Poisson distribution if and only if it mass function is equal to (Elion et al, 2016;Batsindila et al, 2019 andMandangui et al,2019)…”

Section: Definition: the Crossing Methodsmentioning

confidence: 99%

The New Bivariate Conway-Maxwell-Poisson Distribution Obtained by the Crossing Method

Bidounga¹,

Maloumbi²,

Kitoti³

et al. 2020

IJSP

Self Cite

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“…When the basic distribution is equal to the univariate Poisson distribution of parameter δ, the Expression (1) is called the univariate weighted Poisson distribution. The univariate weighted Poisson distribution has the following characteristics [3]:…”

Section: Univariate Weighted Poisson Distributionmentioning

confidence: 99%

“…The resolution of these models makes it possible to highlight, not only the independence between the variables Y 1 and Y 2 but also the effect of the factor x on these same variables. The bivariate Poisson distribution according to [4] has the following characteristics [3]:…”

Section: Generalized Poisson Distributionmentioning

confidence: 99%

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A Note on the (Weighted) Bivariate Poisson Distribution

Bidounga

Nganga²,

Niéré³

et al. 2021

Eur. J. Pure Appl. Math.

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In the recent statistical literature, the univariate Poisson distribution has been generalized by many authors, among them: the univariate weighted Poisson distribution [13], the generalized univariate Poisson distribution [7], the bivariate Poisson distribution according to Holgate [11], the bivariate Poisson distribution according to Lakshminarayana, Pandit and Srinivasa Rao [15], the bivariate Poisson distribution according to Berkhout and Plug [4], the bivariate weighted Poisson distribution according to Elion et al. [8] and the generalized bivariate Poisson distribution according to Famoye [9]. In this paper, We highlight the weighted bivariate Poisson distribution and show that it is the synthesis of all the bivariate Poisson distributions which, under certain conditions, converge in distribution towards the bivariate Poisson distribution according to Berkhout and Plug [4] which can be considered like the standard distribution in N2 as is the univariate Poisson distribution in N.

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GNSS/Inertial Navigation/Wireless Station Fusion UAV 3-D Positioning Algorithm With Urban Canyon Environment

et al. 2022

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The covariance structure of the bivariate weighted Poisson distribution and application to the Aleurodicus data

Cited by 3 publications

References 7 publications

The New Bivariate Conway-Maxwell-Poisson Distribution Obtained by the Crossing Method

The New Bivariate Conway-Maxwell-Poisson Distribution Obtained by the Crossing Method

A Note on the (Weighted) Bivariate Poisson Distribution

GNSS/Inertial Navigation/Wireless Station Fusion UAV 3-D Positioning Algorithm With Urban Canyon Environment

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