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A New Class of Alternative Bivariate Kumaraswamy-Type Models: Properties and Applications

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  • Indranil Ghosh

    (Department of Mathematics and Statistics, University of North Carolina, Wilmington, NC 28403, USA)

Abstract

In this article, we introduce two new bivariate Kumaraswamy (KW)-type distributions with univariate Kumaraswamy marginals (under certain parametric restrictions) that are less restrictive in nature compared with several other existing bivariate beta and beta-type distributions. Mathematical expressions for the joint and marginal density functions are presented, and properties such as the marginal and conditional distributions, product moments and conditional moments are obtained. Additionally, we show that both the proposed bivariate probability models have positive likelihood ratios dependent on a potential model for fitting positively dependent data in the bivariate domain. The method of maximum likelihood and the method of moments are used to derive the associated estimation procedure. An acceptance and rejection sampling plan to draw random samples from one of the proposed models along with a simulation study are also provided. For illustrative purposes, two real data sets are reanalyzed from different domains to exhibit the applicability of the proposed models in comparison with several other bivariate probability distributions, which are defined on [ 0 , 1 ] × [ 0 , 1 ] .

Suggested Citation

  • Indranil Ghosh, 2023. "A New Class of Alternative Bivariate Kumaraswamy-Type Models: Properties and Applications," Stats, MDPI, vol. 6(1), pages 1-21, January.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:1:p:14-252:d:1051184
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    References listed on IDEAS

    as
    1. Barry C. Arnold & Indranil Ghosh, 2017. "Some alternative bivariate Kumaraswamy models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9335-9354, September.
    2. Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    3. Saralees Nadarajah, 2007. "A new bivariate beta distribution with application to drought data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 153-174.
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