In recent decades, many families of distributions and, consequently, new distributions are proposed in order to provide a good flexibility and fit to real data sets. However, several of these distributions have a complicated shape to express their probability density function (pdf) and cumulative distribution function (cdf). Examples of families that involve such functions are: beta-G (see Eugene et al. Beta normal distribution and its applications. Commun Stat - Theory Methods. 2006;31:497–512, for example) and gamma-G (for more details, see Nadarajah et al. The Zografos–Balakrishnan-G family of distributions: mathematical properties and application. Commun Stat - Theory Methods. 2015;44:186–215) families. In this sense, we introduce a new bounded distribution by using a mixture of power function and continuous logarithmic distribution, named as the power logarithmic (PL) distribution, that has a simple form in the expressions of its pdf and cdf. Various statistical and mathematical properties of the new model are obtained in closed form, which is a very positive aspect when we propose a new model. Based on the basic properties, two new characterizations of the new model will be given. Finally, the applicability of PL model to modelling real data is proved by two real data sets, showing the good fit of the new distribution, when compared with others already know in the literature.

近几十年来，为了提供良好的灵活性并适合实际数据集，提出了许多分布族，因此提出了新的分布。但是，这些分布中的一些分布具有复杂的形状来表示其概率密度函数（pdf）和累积分布函数（cdf）。涉及这种功能的家族的例子有：β- G（参见Eugene等人，β正态分布及其应用。例如，Commun Stat-Theory Methods。2006; 31：497-512）和gamma- G（有关更多详细信息，请参见Nadarajah等人。Zografos–Balakrishnan-G分布族：数学性质和应用。Commun Stat-Theory Methods。2015; 44：186–215）族。从这个意义上讲，我们通过使用幂函数和连续对数分布的混合来引入新的有界分布，称为幂对数（PL）分布，在pdf和cdf表达式中具有简单形式。新模型的各种统计和数学属性以封闭形式获得，这在我们提出新模型时是非常积极的方面。基于基本属性，将给出新模型的两个新特征。最后，通过两个真实数据集证明了PL模型对真实数据建模的适用性，显示了新分布的良好拟合，