Abstract
In this paper, we have obtained the Bayes Estimator of Generalized-Exponential scale and shape parameter using Lindley's approximation (L-approximation) under asymmetric loss functions. The proposed estimators have been compared with the corresponding MLE for their risks based on simulated samples from the Generalized-Exponential distribution.
Highlights
Exponential distribution is the most exploited distribution for life data analysis, but its suitability is restricted to constant hazard rate
One of the major disadvantages of the gamma distribution is that its distribution and survival functions cannot be expressed in a closed form if the shape parameter is not an integer
The maximum likelihood estimators and risks of the estimators cannot be put in a convenient closed form
Summary
Exponential distribution is the most exploited distribution for life data analysis, but its suitability is restricted to constant hazard rate. For situations where the failure rate is monotonically increasing or decreasing, two-parameter Weibull and Gamma are the most popular distributions used for analyzing any lifetime data. In the estimation of reliability and failure rate functions, an overestimation is usually much more serious than an underestimation In this case, the use of symmetrical loss function might be inappropriate as emphasized by Basu and Ebrahimi (1991). A useful asymmetric loss known as the LINEX loss function (linear-exponential) was introduced by Varian (1975) and has been widely used by several authors, Zellner (1986), Basu and Ebrahimi (1991), Calabria and Pulcini (1996), Soliman (2002), Singh et al (2005), and Ahmadi et al (2005). Our aim in this paper is to propose a Bayes estimator of the parameter of Generalized-Exponential distribution under the LINEX loss function using Lindley’s approximation technique.
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