Bivariate Discrete Distributions

Kocherlakota, Subrahmaniam; Kocherlakota, Kathleen

doi:10.1201/9781315138480

Cited by 51 publications

(69 citation statements)

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“…The bivariate distributions we discuss are constructed by what we will generally call “latent-variate reduction.” In the bivariate case, this is known in the literature as “trivariate reduction” because it models the two observable variables in terms of three independent latent variables (e.g., Kocherlakota & Kocherlakota, 1992). In Supplementary Appendix B (Online Resource 1), we derive the bivariate Poisson distribution (Teicher, 1954; Holgate, 1964), which involves fewer parameters and therefore provides a slightly simpler illustration of latent-variate reduction than that presented below.…”

Section: Latent-variate Reduction: Bivariate Lgp and Bivariate Negatimentioning

confidence: 99%

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Applying Multivariate Discrete Distributions to Genetically Informative Count Data

Kirkpatrick

Neale

2015

Behav Genet

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We present a novel method of conducting biometric analysis of twin data when the phenotypes are integer-valued counts, which often show an L-shaped distribution. Monte Carlo simulation is used to compare five likelihood-based approaches to modeling: our multivariate discrete method, when its distributional assumptions are correct, when they are incorrect, and three other methods in common use. With data simulated from a skewed discrete distribution, recovery of twin correlations and proportions of additive genetic and common environment variance was generally poor for the Normal, Lognormal and Ordinal models, but good for the two discrete models. Sex-separate applications to substance-use data from twins in the Minnesota Twin Family Study showed superior performance of two discrete models. The new methods are implemented using R and OpenMx and are freely available.

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Section: Latent-variate Reduction: Bivariate Lgp and Bivariate Negatimentioning

confidence: 99%

“… 1 This is not the same as the bivariate negative binomial distribution of Kocherlakota & Kocherlakota (1992), which is actually a special case of the negative multinomial distribution (Johnson, Kotz, & Balakrishnan, 1997). …”

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confidence: 99%

Applying Multivariate Discrete Distributions to Genetically Informative Count Data

Kirkpatrick

Neale

2015

Behav Genet

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“…On the other hand, the bivariate distributions have been derived and discussed by many authors which have many applications in the areas such as engineering, reliability, sports, weather, drought, among others. Until now, many continuous bivariate distributions based on Marshall and Olkin (1976) Also, many discrete bivariate distributions have been introduced, see Kocherlakota and Kocherlakota (1992), Kumar (2008), Kemp (2013), Lee and Cha (2015), Nekoukhou and Kundu (2017), among others.…”

Section: Introductionmentioning

confidence: 99%

Bivariate exponentiated discrete Weibull distribution: statistical properties, estimation, simulation and applications

et al. 2019

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In this paper, a new bivariate discrete distribution is introduced which called bivariate discrete exponentiated Weibull (BDEW) distribution. Several of its mathematical statistical properties are derived such as the joint cumulative distribution function, the joint joint hazard rate function, probability mass function, joint moment generating function, mathematical expectation and reliability function for stress-strength model. Further, the parameters of the BDEW distribution are estimated by the maximum likelihood method. Two real data sets are analyzed, and it was found that the BDEW distribution provides better fit than other discrete distributions.

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“…Several definitions for the BPD have been given (see, e.g. Kocherlakota and Kocherlakota, 1992). In this paper we will work with the following one, because it has received the most attention in the statistical literature (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Goodness-of-fit tests for the bivariate Poisson distribution

Novoa-Muñoz

2019

Communications in Statistics - Simulation and Computation

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The bivariate Poisson distribution is commonly used to model bivariate count data. In this paper we study a goodness-of-fit test for this distribution. We also provide a review of the existing tests for the bivariate Poisson distribution, and its multivariate extension.The proposed test is consistent against any fixed alternative. It is also able to detect local alternatives converging to the null at the rate n − 1 2 . The bootstrap can be employed to consistently estimate the null distribution of the test statistic. Through a simulation study we investigated the goodness of the bootstrap approximation and the power for finite sample sizes.

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Bivariate Discrete Distributions

Cited by 51 publications

References 0 publications

Applying Multivariate Discrete Distributions to Genetically Informative Count Data

Applying Multivariate Discrete Distributions to Genetically Informative Count Data

Bivariate exponentiated discrete Weibull distribution: statistical properties, estimation, simulation and applications

Goodness-of-fit tests for the bivariate Poisson distribution

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