Department of Mathematics, Bartin University, Bartin, Turkey.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia.
PLoS One. 2021 Jan 22;16(1):e0245627. doi: 10.1371/journal.pone.0245627. eCollection 2021.
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.
引入了一个新的定义在（0,1）区间上的分布。它的概率密度和累积分布函数具有简单的形式。由于其简单的形式，提出的分布的矩、不完全矩和分位数函数被推导出来，并以显式形式得到。使用了四种参数估计方法来估计分布的未知参数。此外，还进行了模拟研究来比较这些参数估计方法的效率。更重要的是，由于提出的分布，我们为有界响应变量提供了一种替代的回归模型。基于两个真实数据集，将提出的回归模型与 beta 和 unit-Lindley 回归模型进行了比较。
