Abstract
In this paper, we introduce a new class of lifetime distributions which is called the additive Weibull geometric (AWG) distribution. This distribution obtained by compounding the additive Weibull and geometric distributions. The new distribution has a number of well-known lifetime special sub-models such as modified Weibull geometric, Weibull geometric, exponential geometric, among several others. Some structural properties of the proposed new distribution are discussed. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.
Highlights
The study of life length of organisms, structures, materials, etc., is very important in the biological and engineering sciences
We introduce a new class of lifetime distributions which is called the additive Weibull geometric (AWG) distribution
We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix
Summary
The study of life length of organisms, structures, materials, etc., is very important in the biological and engineering sciences. The Weibull distribution, having exponential and Rayleigh as special cases, is a very popular distribution for modeling lifetime data and for modeling phenomenon with monotone failure rates. The Weibull distribution does not provide a reasonable parametric fit for modeling phenomenon with non-monotone failure rates such as the bathtub-shaped and the unimodal failure rates which are common in reliability and biological studies. Such bathtub hazard curves have nearly flat middle portions and the corresponding densities have a positive anti-mode. We propose a new lifetime distribution, referred to as the additive Weibull geometric (AAA) distribution which contains as special sub-models and study some of its properties.
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