Inverted Exponential Distribution Under a Bayesian Viewpoint

The objective of this study was to examine the properties of Bayes estimators of the parameter, reliability function and hazard rate under the symmetric and asymmetric loss functions for the inverted exponential model. The Bayes predictive interval and the Bayes estimate of shift point are also determined. A simulation study was carried out to study the properties of the Bayes estimators. Introduction The exponential distribution is frequently used in lifetime data analysis, but its suitability is restricted to constant hazard (failure) rates. For situations where a failure rate is monotonically increasing or decreasing, the two-parameter Weibull and the Gamma distributions are popular for analyzing lifetime data. Both distributions have increasing and decreasing hazard rates depending on the shape parameter. However, 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. Moreover, there are terms involving the incomplete Gamma function, thus, it is necessary to obtain distribution, survival or hazard functions by numerical integration. This makes the Gamma distribution less popular compared to the Weibull distribution, which has a closed form for the hazard and survival functions, but the Weibull distribution also has disadvantages. Bain & Engelhardt (1991) demonstrated that the maximum likelihood estimators of the Weibull distribution might not behave properly for all parametric ranges. Recently two new distributions have been introduced: the generalized Exponential (two-parameter) and the inverted Exponential (one-parameter) distributions. The generalized