An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data

Abstract

In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models are introduced and studied. We show that the GLL density is rewritten as a two-member linear combination of the exponentiated G-densities and that, consequently, many of its mathematical properties arise directly, such as moment-based expressions. A maximum likelihood estimation procedure for the GLL parameters is provided and the behavior of the resulting estimates is evaluated by Monte Carlo experiments. An application to repairable data is made. The results argue for the use of the exponential law as the basis for the GLL-G family.

A Flexible Extension of Reduced Kies Distribution: Properties, Inference, and Applications in Biology

“…According to the literature, a number of distributions with support on the unit interval have been presented, which are derived from transformations of the cumulative distribution function (CDF). Many writers have developed and examined unit distributions such as unit Teissier distribution [1], exponentiated Topp-Leone distribution [2], log-Lindley distribution [3], transformed gamma distribution [4], Cosine-sine distribution [5], power log-Lindley distribution, power logarithmic distribution and unit Weibull distribution [6,7,8], respectivly.…”