A New Generalized Log-logistic and Modified Weibull Distribution with Applications

Abstract

A new generalized distribution called the log-logistic modified Weibull (LLoGMW) distribution is presented. This distribution includes many submodels such as the log-logistic modified Rayleigh, log-logistic modified exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh and exponential distributions as special cases. Structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and Rényi entropy are derived. Model parameters are estimated based on the method of maximum likelihood. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.

Application of the Exponentiated Log-Logistic Weibull Distribution to Censored Data

“…In this section, the generalized or exponentiated log-logistic Weibull (ELLoGW) distribution is presented. The generalized or exponentiated log-logistic Weibull (ELLoGW) (see Oluyede et al [1] for details) distribution function is given by…”

“…Oluyede et al had recently proposed a new model called the Exponentiated Log-Logistic Weibull (ELLoGW) distribution with applications to reliability, survival analysis and income data [1]. In this paper, we are primarily concerned with the application of the new model (ELLoGW) to censored data.…”

“…In this paper, we are primarily concerned with the application of the new model (ELLoGW) to censored data. The details of the model and all its associated properties including the hazard function, reverse hazard function, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, entropy and order statistics have been reported earlier [1].…”

“…Generally, the data obtained under these or similar scenarios are called censored data. Literature is replete on application of statistical distribution to different types of data [1,4,5,6]. A brief review of the model, the different types of censored data and the application of the model to different types of censored data are discussed in the subsequent sections.…”

A New Generalized- X Family for Analyzing the COVID-19 Data Set: a Case Study

“…In this credit, the development and introduction of new families of distribution have received much attention. e new families are developed by introducing new parameters [1][2][3][4].…”