Abstract
A new six-parameter distribution called the beta generalized inverse Weibull-geometric distribution is proposed. The new distribution is generated from the logit of a beta random variable and includes the generalized inverse Weibull geometric distribution.Various structural properties of the new distribution including explicit expressions for the moments, moment generating function, mean deviation are derived. The estimation of the model parameters is performed by maximum likelihood method.
Highlights
The inverse Weibull (IW) distribution has many applications in the reliability engineering discipline and model degradation of mechanical components such as the dynamic components
Based on compounding the generalized IW (GIW) distribution with the Gc distribution and using the beta-G (B-G) family pioneered by Eugene et al (2002), we construct the six-parameter beta generalized inverse Weibull geometric (BGIWGc) model and give a comprehensive description of some of its mathematical properties
In this subsection we present a useful linear representation for the BGIWGc pdf
Summary
The inverse Weibull (IW) distribution has many applications in the reliability engineering discipline and model degradation of mechanical components such as the dynamic components (pistons, crankshafts of diesel engines, etc). There have been many attempts to define new families of probability distributions that extend well-known families of distributions and at the same time provide great flexibility in modeling data in practice. We define and study a new lifetime model called the beta generalized inverse Weibull geometric (BGIWGc) distribution. Based on compounding the GIW distribution with the Gc distribution and using the beta-G (B-G) family pioneered by Eugene et al (2002), we construct the six-parameter BGIWGc model and give a comprehensive description of some of its mathematical properties. Consider the failure times of the initial defects, denoted by be independent and identically distributed (iid) random variables following the GIW distribution with cdf and pdf (1).
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