Abstract
A new distribution, the so called beta exponentiated Weibull geometric (BEWG) distribution is proposed. The new distribution is generated from the logit of a beta random variable and includes the exponentiated Weibull geometric distribution as particular case. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the model was showed by using a real dataset. In order to validate the results a simulation bootstrap is presented in this paper.
Highlights
Introduction and motivationLet G(x; φ) be the cumulative distribution function of an absolutely continuous random variable following the distribution G, where φ ∈ Ω is the parameter vector
The beta exponentiated Weibull geometric distribution is very flexible model that approaches to different distributions when its parameters are changed
In this paper we have introduced a new distribution called beta exponentiated Weibull-geometric (BEWG) distribution
Summary
Let G(x; φ) be the cumulative distribution function (cdf) of an absolutely continuous random variable following the distribution G, where φ ∈ Ω is the parameter vector. (CORDEIRO; SILVA; ORTEGA, 2011) introduced the beta-Weibull geometric distribution with G(x; φ) in (1) to be the cdf of the Weibullgeometric distribution of (BARRETO-SOUZA; MORAIS; CORDEIRO, 2011). (BIDRAM; BEHBOODIAN; TOWHIDI, 2013) introduced new distribution generated from the logit of a beta random variable and includes the Weibull geometric distribution of (BARRETO-SOUZA; MORAIS; CORDEIRO, 2011). (MAHMOUDI; SHIRMAN, 2012) compounded an exponentiated Weibull distribution with a geometric distribution and obtained a new lifetime distribution with hazard rate function can be decreasing, increasing, bathtube and unimodal. Such bathtub hazard curves have nearly flat middle portions and the corresponding densities have a positive anti-mode.
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