The unit-Cauchy quantile regression model with variates observed on (0, 1): percentages, proportions, and fractions

Year 2025, Early Access, 1 - 23

Talha Arslan , Keming Yu

https://doi.org/10.15672/hujms.1533205

Abstract

In this study, a new parametric quantile regression model is introduced as an alternative to the beta regression and Kumaraswamy quantile regression model. The proposed quantile regression model is obtained by reparametrization of the unit-Cauchy distribution in terms of its quantiles. The model parameters are estimated using the maximum likelihood method. A Monte-Carlo simulation study is conducted to show the efficiency of the maximum likelihood estimation of the model parameters. The implementation of the proposed quantile regression model is shown by using real datasets. Quantile regression models based on unit-Weibull, unit generalized half normal, and unit Burr XII are also considered in the applications. The application results show that the proposed quantile regression model is preferable over its rivals when several comparison criteria are taken into account. In addition, the fitting plots indicate that the proposed quantile regression model fits extreme observations on the right tail better than its strong rivals, which is important in quantile regression modeling.

Keywords

Quantile regression, Monte-Carlo simulation, Maximum likelihood, Parametric model, Unit-Cauchy

Thanks

The editor and reviewers are thanked for comments that led to presentational improvements. Talha Arslan would like to thank Brunel University London (UK) for a visiting position in 2023 to collaborate with Prof. Keming Yu and providing a peaceful environment to conduct this study.

References

• [1] T. Arslan, A new family of unit-distribution: Definition, properties and applications, TWMS J. App. Eng. Math. 13 (2), 782–791, 2023.