Some mew and generalized families of probability distributions with applications

Abstract

Some new generalized distributions called the new Gamma Lindley-Log-logistic (GLLLoG) distribution, new Weibull Generalised-G (NWG-G) family of distributions and the Exponentiated Half-Logistic Odd Lindley-G family of distributions are proposed and presented. These distributions contain several distributions such as Half-Logistic, Odd Lindley, Lindley, Log-Logistic, new-Rayleigh generalized-G, new exponential generalized-G, new Rayleigh-G and the new-Weibull-G family of distributions. A comprehensive investigation of the properties of these generalized distributions including series expansion of pdfs, cdfs, moments, hazard functions, quantile functions, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, Renyi entropy and ´ distribution of order statistics are presented. Model parameters are estimated using maximum likelihood estimation technique and real datasets are used to illustrate the potentiality of the three new generalized distributions compared with other distributions.