Marshall-Olkin Log-Logistic Extended Weibull Distribution : Theory, Properties and Applications

Abstract

Marshall and Olkin (1997) introduced a general method for obtaining more flexible distributions by adding a new parameter to an existing one, called the Marshall-Olkin family of distributions. We introduce a new class of distributions called the Marshall-Olkin Log-Logistic Extended Weibull (MOLLEW) family of distributions. Its mathematical and statistical properties including the quantile function hazard rate functions, moments, conditional moments, moment generating function are presented. Mean deviations, Lorenz and Bonferroni curves, Rényi entropy and the distribution of the order statistics are given. The Maximum likelihood estimation technique is used to estimate the model parameters and a special distribution called the Marshall-Olkin Log Logistic Weibull (MOLLW) distribution is studied, and its mathematical and statistical properties explored. Applications and usefulness of the proposed distribution is illustrated by real datasets.

The Marshall-Olkin-Topp-Leone-Gompertz-G Family of Distributions with Applications

“…Some of those generalizations include the beta Marshall-Olkin-G (BMO-G) distribution by Alizadeh et al [3], Kumaraswamy Marshall-Olkin-G (KwMO-G) distribution by Alizadeh et al [4] and Marshall-Olkin Half Logistic-G (MOHL-G) distribution by Makubate et al [26]. A new class of distributions called the Marshall-Olkin Loglogistic Extended Weibull (MOLLEW) family of distributions was proposed by Lepetu et al [25]. Chakraborty and Handique [9] presented the generalized Marshall-Olkin Kumaraswamy-G distribution, and the ratio and inverse 883 moments of Marshall-Olkin extended Burr Type III distribution based on lower generalized order statistics was proposed by Kumar [22].…”

Marshall-Olkin-Odd Power Generalized Weibull-G Family of Distributions with Applications of COVID-19 Data

“…Santos-Neto et al [29] introduces a new class of models called the Marshall-Olkin extended Weibull family of distributions which defines at least twenty-one special models. Lepetu et al [19] proposed the Marshall-Olkin Log-Logistic Extended Weibull distribution. Usman and Haq [30] studied the Marshall-Olkin extended inverted Kumaraswamy distribution and Javed et al [13] developed the Marshall-Olkin Kappa distribution.…”

Marshall-Olkin-Type II-Topp-Leone-G Family of Distributions: Model, Properties and Applications

“…Generalizations of the Marshall-Olkin distribution include Kumaraswamy Marshall-Olkin-G by Alizadeh et al [5], Beta Marshall-Olkin-G by Alizadeh et al [4], Marshall-Olkin Log-logistic Extended Weibull by Lepetu et al [16], Marshall-Olkin-Extended Burr Type III distribution by Kumar et al [15], Marshall-Olkin Log-logistic Erlang-Truncated Exponential by Oluyede et al [22] and Marshall-Olkin-Gompertz-G by Chipepa and Oluyede [12] to name a few.…”