The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates

ABSTRACT

The Beta distribution is the standard model for quantifying the influence of covariates on the mean of a response variable on the unit interval. However, this well-known distribution is no longer useful when we are interested in quantifying the influence of such covariates on the quantiles of the response variable. Unlike Beta, the Kumaraswamy distribution has a closed-form expression for its quantile and can be useful for the modeling of quantiles in the absence/presence of covariates. As an alternative to the Kumaraswamy distribution for the modeling of quantiles, in this paper the unit-Weibull distribution was considered. This distribution was obtained by the transformation of a random variable with Weibull distribution. The same transformation applied to a random variable with Exponentiated Exponential distribution generates the Kumaraswamy distribution. The suitability of our proposal was demonstrated to model quantiles, conditional on covariates, with two simulated examples and three real applications with datasets from health, accounting and social science. For such data sets, the obtained fits of the proposed regression model were compared with those provided by the Beta and Kumaraswamy regression models.

KEYWORDS:

• Beta regression
• unit-Weibull distribution
• Kumaraswamy quantile regression
• likelihood
• model selection

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Acknowledgments

The authors are thankful to the referees for many valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

J. Mazucheli http://orcid.org/0000-0001-6740-0445

R. P. de Oliveira http://orcid.org/0000-0001-6134-5975

Additional information

Funding

Josmar Mazucheli gratefully acknowledge the partial financial support from Fundação Araucária (grant 064/2019 – UEM/Fundação Araucária).