Marshall-Olkin extended log-logistic distribution and its application in minification processes

Abstract

In this paper, a new class of Log-Logistic distribution using Marshall-Olkin transformation is introduced. Its characterization and statistical properties are obtained. The proposed model extends the Log-Logistic distribution and is more flexible. Using the proposed model, we construct an autoregressive model and investigate its minification structure.

The Lomax generator of distributions: Properties, minification process and regression model

“…Several authors derived new distributions using the Marshal-Olkin method applied to the theory of minification processes. Some recent results are: the Marshall-Olkin log-logistic minification process [17], Marshall-Olkin q-Weibull distribution and max-min processes [20,21], Marshall-Olkin beta distribution and its applications (Jose et al, 2009), Marshall-Olkin gamma minification process [27] and Marshall-Olkin semi-Weibull minification process (Thomas and Jose, 2005). Cifarelli et al [7] proposed generalized semi-Pareto and semi-Burr distributions and random coefficient minification processes.…”

Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution

“…The MO transformation provides an extra parameter which yields a better …t with di¤erent types of data than baseline distribution. MO extended distributions and their applications have been extensively studied in the literature such as [4,9,10,11,12,14,24]. The MO transformation is de…ned as given in below.…”

Marshall-Olkin extended Burr III distribution

“…Several studies have been conducted to propose several distribution extensions and discussed their properties and inference. These includes the Marshall-Olkin extended (MOE) Weibull proposed by Ghitany et al [9], MOE Pareto proposed by Ghitany [7], MOE gamma proposed by Ristic et al [15], MOE Lomax using censored data proposed by Ghitany et al [8], MOE exponential distribution proposed by Srivastava et al [19], MOE Uniform distribution proposed by Jose and Krishna [12], both MOE power log-normal and MOE log-logistic distributions proposed by Gui [10], [11], and MOE Burr type XII distribution proposed by Al-Saiari et al [1]. In addition, Santos-Neto et al [16] introduced the MOE Weibull family of distributions and studied some of its mathematical properties.…”