A New Generalized Family of Weibull-Exponentiated Half Logistic-G Distribution with Applications

Abstract

We propose a new extension of the Weibull-exponentiated half logistic-G
(WEHL-G) distribution, called the Marshall-Olkin-Weibull-exponentiated half
logistic-G (MO-WEHL-G) family of distributions. The properties of this family
of distributions including quantile function, distribution of the order statistics,
hazard rate function, Rényi entropy and moments of residual life are presented.
To estimate the parameters of the MO-WEHL-G family of distributions,
six different estimation approaches are used, namely, maximum likelihood,
Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, Cramérvon Mises and Maximum Product of Spacing. The consistency properties of
the six estimation methods were assessed using Monte Carlo simulations for a
special case of the MO-WEHL-G family of distributions. The flexibility and
importance of the proposed model was assessed using numerous goodness-of-fit
statistics on three different data sets.