Journal
STATISTICAL PAPERS
Volume 54, Issue 1, Pages 177-192Publisher
SPRINGER
DOI: 10.1007/s00362-011-0417-y
Keywords
Kumaraswamy distribution; Beta distribution; Median-dispersion parameterization; Quantile-spread order; Limiting distributions; Regression modeling; Generalized linear models; Latent-variable models; Simulation-based estimation methods
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The Kumaraswamy distribution is very similar to the Beta distribution, but has the important advantage of an invertible closed form cumulative distribution function. The parameterization of the distribution in terms of shape parameters and the lack of simple expressions for its mean and variance hinder, however, its utilization with modeling purposes. The paper presents two median-dispersion re-parameterizations of the Kumaraswamy distribution aimed at facilitating its use in regression models in which both the location and the dispersion parameters are functions of their own distinct sets of covariates, and in latent-variable and other models estimated through simulation-based methods. In both re-parameterizations the dispersion parameter establishes a quantile-spread order among Kumaraswamy distributions with the same median and support. The study also describes the behavior of the re-parameterized distributions, determines some of their limiting distributions, and discusses the potential comparative advantages of using them in the context of regression modeling and simulation-based estimation.
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