Abstract
A new continuous version of the inverse flexible Weibull model is proposed and studied. Some of its properties such as quantile function, moments and generating functions, incomplete moments, mean deviation, Lorenz and Bonferroni curves, the mean residual life function, the mean inactivity time, and the strong mean inactivity time are derived. The failure rate of the new model can be “increasing-constant,” “bathtub-constant,” “bathtub,” “constant,” “J-HRF,” “upside down bathtub,” “increasing,” “upside down-increasing-constant,” and “upside down.” Different copulas are used for deriving many bivariate and multivariate type extensions. Different non-Bayesian well-known estimation methods under uncensored scheme are considered and discussed such as the maximum likelihood estimation, Anderson Darling estimation, ordinary least square estimation, Cramér-von-Mises estimation, weighted least square estimation, and right tail Anderson Darling estimation methods. Simulation studies are performed for comparing these estimation methods. Finally, two real datasets are analyzed to illustrate the importance of the new model.
Highlights
Introduction eWeibull model [1] is a very useful distribution in modeling real data exhibiting monotonic hazard rate function (HRF)
Bebbington et al [2] have defined a new two-parameter distribution which is an extension of the Weibull distribution referred to as a flexible Weibull (FW) extension distribution; it has a failure function that can be “decreasing,” “increasing,” or “bathtub-shaped.”
El-Gohary et al [3] proved that the hazard rate function (RRF) of the inverse flexible Weibull (IFW) model can be “upside down constant,” the cumulative distribution function (CDF) of IFW distribution is given by α
Summary
1. Introduction e Weibull model [1] is a very useful distribution in modeling real data exhibiting monotonic hazard rate function (HRF). Introduction e Weibull model [1] is a very useful distribution in modeling real data exhibiting monotonic hazard rate function (HRF) It cannot be used in modeling and studying data which have nonmonotonic HRF such as the “bathtub shape (U-HRF).”. For avoiding this drawback, Bebbington et al [2] have defined a new two-parameter distribution which is an extension of the Weibull distribution referred to as a flexible Weibull (FW) extension distribution; it has a failure function that can be “decreasing,” “increasing,” or “bathtub-shaped.”.
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