The McDonald Generalized Beta-Binomial Distribution: A New Binomial Mixture Distribution and Simulation Based Comparison with Its Nested Distributions in Handling Overdispersion

Chandrabose, Manoj; Wijekoon, Pushpakanthie; Yapa, Roshan Darshana

doi:10.5539/ijsp.v2n2p24

Cited by 7 publications

(4 citation statements)

References 25 publications

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“…We employ the finite series representation of the McDonald's Generalized Beta-Binomial distribution as presented in Manoj et al (2013). The McGBB has considerable improvement over the BB, KPI and KPII models.…”

Section: Discussionmentioning

confidence: 99%

“…(2013). Some theoretical properties of McGBB are already discussed in Manoj et al (2013) would not again be discussed here. The parameters of the McGBB distribution are estimated via maximum likelihood estimation technique.…”

Section: Introductionmentioning

confidence: 99%

“…The Kumaraswamy-Binomial (KB) distribution (Kumuraswamy, 1980) is another well utilized member of this class. In this paper we focus the emphasis on the McDonald's Generalized Beta distribution (Manjor et al, 2015) of the first kind as the mixing distribution and would employ the newly introduced the McDonald Generalized Beta-Binomial distribution(McGBB) Manoj al. (2013).…”

Section: Introductionmentioning

confidence: 99%

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On Some Mixture Models for Over-dispersed Binary Data

Lawal¹

2017

IJSP

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In this paper, we consider several binomial mixture models for fitting over-dispersed binary data. The models range from the binomial itself, to the beta-binomial (BB), the Kumaraswamy distributions I and II (KPI & KPII) as well as the McDonald generalized beta-binomial mixed model (McGBB). The models are applied to five data sets that have received attention in various literature. Because of convergence issues, several optimization methods ranging from the Newton-Raphson to the quasi-Newton optimization algorithms were employed with SAS PROC NLMIXED using the Adaptive Gaussian Quadrature as the integral approximation method within PROC NLMIXED. Our results differ from those presented in Li, Huang and Zhao (2011) for the example data sets in that paper but agree with those presented in Manoj, Wijekoon and Yapa (2013). We also applied these models to the case where we have a k vector of covariates (x 1 , x 2 , . . . , x k ) ′ . Our results here suggest that the McGBB performs better than the other models in the GLM framework.All computations in this paper employed PROC NLMIXED in SAS. We present in the appendix a sample of the SAS program employed for implementing the McGBB model for one of the examples.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Some Mixture Models for Over-dispersed Binary Data

Lawal¹

2017

IJSP

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“…To overcome this problems, several distributions have been utilized, especially mixture models such as the beta-binomial in [1], the Kumarasmawany in [2] and most recently the McDonald's generalized beta-distribution (McGBB) in [3]. Each of these distributions, separately models the probability of success π with beta, Kumaraswany, and exponential (continuous type) distributions respectively.…”

Section: Introductionmentioning

confidence: 99%

Employing the Double, Multiplicative and The Com-Poisson Binomial Distributions for modeling Over and Under-dispersed Binary Data

Lawal

2017

JAMCS

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In this paper, we compare the performances of several models for fitting over-dispersed binary data. The distribution models considered in this study include the binomial (BN), the betabinomial (BB), the multiplicative binomial (MBM), the Com-Poisson binomial (CPB) and the double binomial (DBM) models. Applications of these models to several well known data sets exhibiting under-dispersion and over-dispersion were considered in this paper. We applied these models to two frequency data sets and two data sets with covariates that have been variously analysed in the literature. The first relates to the Portuguese version of Duke Religiosity Index in a sample of 273 (202 women, 71 Male) postgraduate students of the faculty of Medicine of University of Sao Paulo. The second set that employs the Generalize Linear Model (GLM) is the correlated binary data which studies the cardiotoxic effects of doxorubicin chemoteraphy on the treatment of acute lymphoblastic leukemia in childhood. In the first data set, we have a single covariate, Sex (0,1) and two covariates in the second data set (dose and time). Our results indicate that all the models considered here (excluding the binomial) behave reasonably well in modeling over-dispersed binary data with or without covariates, although both the multiplicative binomial and the double binomial models slightly behave better for these

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The two-sided power-binomial distribution for modeling binary count data

Genç

2018

Communications in Statistics - Theory and Methods

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The McDonald Generalized Beta-Binomial Distribution: A New Binomial Mixture Distribution and Simulation Based Comparison with Its Nested Distributions in Handling Overdispersion

Cited by 7 publications

References 25 publications

On Some Mixture Models for Over-dispersed Binary Data

On Some Mixture Models for Over-dispersed Binary Data

Employing the Double, Multiplicative and The Com-Poisson Binomial Distributions for modeling Over and Under-dispersed Binary Data

The two-sided power-binomial distribution for modeling binary count data

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