On the Type-I Half-logistic Distribution and Related Contributions: A Review

The half-logistic (HL) distribution is a widely considered statistical model for studying lifetime phenomena arising in science, engineering, finance, and biomedical sciences. One of its weaknesses is that it has a decreasing probability density function and an increasing hazard rate function only. Due to that, researchers have been modifying the HL distribution to have more functional ability. This article provides an extensive overview of the HL distribution and its generalization (or extensions). The recent advancements regarding the HL distribution have led to numerous results in modern theory and statistical computing techniques across science and engineering. This work extended the body of literature in a summarized way to clarify some of the states of knowledge, potentials, and important roles played by the HL distribution and related models in probability theory and statistical studies in various areas and applications. In particular, at least sixty-seven flexible extensions of the HL distribution have been proposed in the past few years. We give a brief introduction to these distributions, emphasizing model parameters, properties derived, and the estimation method. Conclusively, there is no doubt that this summary could create a consensus between various related results in both theory and applications of the HL-related models to develop an interest in future studies

The Extended Exponentiated Weibull Distribution and its Applications

In this paper, we introduce a univariate four-parameter distribution. Several known distributions like exponentiated Weibull or extended generalized exponential distribution can be obtained as special case of this distribution. The new distribution is quite flexible and can be used quite effectively in analysing survival or reliability data. It can have a decreasing, increasing, decreasing-increasing-decreasing (DID), upside-down bathtub (unimodal) and bathtub-shaped failure rate function depending on its parameters. We provide a comprehensive account of the mathematical properties of the new distribution. In particular, we derive expressions for the moments, mean deviations, Rényi and Shannon entropy. We discuss maximum likelihood estimation of the unknown parameters of the new model for censored and complete sample using the profile and modified likelihood functions. One empirical application of the new model to real data are presented for illustrative purposes

Entropy Estimation of Generalized Half-Logistic Distribution (GHLD) Based on Type-II Censored Samples

This paper derives the entropy of a generalized half-logistic distribution based on Type-II censored samples, obtains some entropy estimators by using Bayes estimators of an unknown parameter in the generalized half-logistic distribution based on Type-II censored samples and compares these estimators in terms of the mean squared error and the bias through Monte Carlo simulations