On a bivariate poisson distribution

Lakshminarayana, J.; Pandit, Soumya; Rao, K. Srinivasa

doi:10.1080/03610929908832297

Cited by 64 publications

(83 citation statements)

References 4 publications

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“…When α 1 = α 2 = 0, this bivariate GP distribution reduces to the bivariate Poisson distribution with the multiplicative factor λ ∈ R developed by Lakshminarayana et al [20].…”

Section: Type I Bivariate Zero-inflated Generalized Poisson Distributmentioning

confidence: 99%

“…The PVC counts for twelve patients one minute after administering a drug with antiarrhythmic properties ( Lakshminarayana et al [20] first proposed a new type of bivariate Poisson distribution, whose joint pmf was expressed as a product of two Poisson margins with a multiplicative factor. Subsequently, a new bivariate negativebinomial regression model and a new bivariate GP distribution are extended in a similar way by Famoye [12,13].…”

Section: Tablementioning

confidence: 99%

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Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Zhang

Tian

Huang

2015

Stat., optim. inf. comput.

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To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP) distributions by incorporating a multiplicative factor (or dependency parameter) λ, named as Type I and Type II bivariate ZIGP λ distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit either positively or negatively correlated and either over-or under-dispersed count data, comparing to the existing models that can only fit positively correlated count data with over-dispersion. The two marginal distributions of Type I bivariate ZIGP λ share a common parameter of zero inflation while the two marginal distributions of Type II bivariate ZIGP λ have their own parameters of zero inflation, resulting in a much wider range of applications. The important distributional properties are explored and some useful statistical inference methods including maximum likelihood estimations of parameters, standard errors estimation, bootstrap confidence intervals and related testing hypotheses are developed for the two distributions. A real data are thoroughly analyzed by using the proposed distributions and statistical methods. Several simulation studies are conducted to evaluate the performance of the proposed methods.

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“…When α 1 = α 2 = 0, this bivariate GP distribution reduces to the bivariate Poisson distribution with the multiplicative factor λ ∈ R developed by Lakshminarayana et al [20].…”

Section: Type I Bivariate Zero-inflated Generalized Poisson Distributmentioning

confidence: 99%

Section: Tablementioning

confidence: 99%

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Zhang

Tian

Huang

2015

Stat., optim. inf. comput.

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“…Most observed frequencies provide (y 1 , 0) and (0, y 2 ) data, indicating negative correlation between y 1 and y 2 . Therefore, we fit BP (Lakshminarayana et al, 1999), BNB (Famoye, 2010) and BPL (Gomez-Deniz et al, 2012) distributions to the data since these distributions can be fitted to bivariate data with positive, zero or negative correlation.…”

Section: Several Testsmentioning

confidence: 99%

“…of BP (θ 1 , θ 2 , α) distribution is (Lakshminarayana et al, 1999): ( , , , , ) a a θ θ α distribution is (Famoye, 2010):…”

Section: Several Testsmentioning

confidence: 99%

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Bivariate Poisson-Lindley Distribution with Application

Zamani¹,

Faroughi

Ismail³

2015

Journal of Mathematics and Statistics

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This study applies a Bivariate Poisson-Lindley (BPL) distribution for modeling dependent and over-dispersed count data. The advantage of using this form of BPL distribution is that the correlation coefficient can be positive, zero or negative, depending on the multiplicative factor parameter. Several properties such as mean, variance and correlation coefficient of the BPL distribution are discussed. A numerical example is given and the BPL distribution is compared to Bivariate Poisson (BP) and Bivariate Negative Binomial (BNB) distributions which also allow the correlation coefficient to be positive, zero or negative. The results show that BPL distribution provides the smallest Akaike Information Criterion (AIC), indicating that the distribution can be used as an alternative for fitting dependent and over-dispersed count data, with either negative or positive correlation.

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The dynamic interdependence in the demand of primary and emergency secondary care: A hidden Markov approach

Laudicella

Donni

2021

J of Applied Econometrics

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Summary This paper develops an extension of the class of finite mixture models for longitudinal count data to the bivariate case by using a hidden Markov chain approach. The model allows for disentangling unobservable time‐varying heterogeneity from the dynamic effect of utilisation of primary and secondary care and measuring their potential substitution effect. Three points of supports adequately describe the distribution of the latent states suggesting the existence of three profiles of low, medium and high users who shows persistency in their behaviour, but not permanence as some switch to their neighbour's profile.

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On a bivariate poisson distribution

Cited by 64 publications

References 4 publications

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Two new bivariate zero-inflated generalized Poisson distributions with a flexible correlation structure

Bivariate Poisson-Lindley Distribution with Application

The dynamic interdependence in the demand of primary and emergency secondary care: A hidden Markov approach

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