Some inferences based on a mixture of power function and continuous logarithmic distribution

Abstract

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.

Keywords

• logarithmic distribution
• moments
• rényi entropy
• characterization