A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models.

Emrah Altun,M S Eliwa,M El-Morshedy,Feng Chen

doi:10.1371/journal.pone.0245627

Emrah Altun, M S Eliwa + Show 2 more

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https://doi.org/10.1371/journal.pone.0245627

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Abstract

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets.

Highlights

In the last decade, modeling of the bounded data sets is increased its popularity
The important question is that do we need this distribution? To answer this question, we summarize the importance of the log-Bilal distribution: (i) the log-Bilal distribution has simple and closed-form expressions for its statistical functions (ii) the properties of the log-Bilal distribution are derived in explicit forms without any special mathematical functions, (iii) the proposed distribution provides more flexibility than existing distributions for the shapes of hazard rate function, (iv) thanks to its simple mathematical functions, we introduce a new regression model based on the log-Bilal density to model the extremely skewed dependent variables with associated covariates
We summarize the concepts of the remaining sections: the moments, incomplete moments, quantile function, and exponential family property of the log-Bilal distribution are obtained

Summary

Introduction

In the last decade, modeling of the bounded data sets is increased its popularity. These kinds of data sets appear in many fields such as finance, actuarial and medical sciences. The statistics literature has very limited distributions defined on (0,1). The best known distributions defined on (0,1) are beta, Topp-Leone by Topp and Leone [1] and Kumaraswamy by Kumaraswamy [2] distributions. To increase the modeling accuracy of the data sets on (0,1), several distributions have been proposed by researchers. The unit-Lindley by Mazucheli et al [3], unit-inverse Gaussian by Ghitany et al [4], unit-Birnbaum-Saunders by Mazucheli et al [5], exponentiated Topp-Leone by Pourdarvish et al [6], transmuted Kumaraswamy by Khan et al [7], log-xgamma by Altun and Hamedani [8], log-weighted exponential by Altun [9] and unitimproved second-degree Lindley by Altun and Cordeiro [10]

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