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

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.

The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model

“…Let define µ = x τ (α, β) and α = log(1 − log τ)(− log µ) −β . Then the re-parameterized cdf and pdf are obtained as G(y, β, µ, τ) = e 1−(1−log τ) (log y/ log µ) β (7) and…”

“…As an example, [6] used X = exp(−T) transformation on the weighted-exponential (WE) distribution and resulting distribution was called as log-WE distribution. Again, [7] used the same transformation for the Bilal distribution and proposed the log-Bilal distribution for extremely left/right skewed data sets defined on the interval (0, 1). Similarly, [8] used X = T/(T + 1) transformation on the improved second-degree Lindley (ISDL) distribution and resulting distribution was called as unit-ISDL distribution.…”

The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications

“…2018 , 2021 ), log-Bilal (Altun et al. 2021 ), log-Lindley (Gómez-Déniz et al. 2014 ), log-weighted exponential (Altun 2021 ), unit-Burr XII (Korkmaz and Chesneau 2021 ), unit Lindley (Mazucheli et al.…”

A Flexible Extension to an Extreme Distribution

“…All of this has encouraged authors to work more on developing new lifetime distributions using different generalization methods. Here, we refer to the papers of [10] for the Marshall-Olkin class, [11] for the Beta and Gamma classes, [12] for the odd exponentiated half-logistic-G (OEHL-G) family, [13] for the flexible Weibull class, [14] for the odd log-logistic Lindley class, [15] for the odd Chen class, [16] for the exponentiated odd Chen class, [17] for a new Kumaraswamy generalized class, [18,19] for the extended Gamma and log-Bilal models, respectively, [20] for type I half logistic odd Weibull-G and [21] for the Poisson transmuted-G family, among others. Here, we use the OEHL-G family of distributions to build a new flexible model with three parameters.…”