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.

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