Abstract
The Exponential distribution has attracted the attention of statisticians working on theory and methods as well as in various fields of lifetime data analysis. In this study, we employ gamma non-informative prior and generalised (data-dependent) non-informative prior proposed by Guure and Ibrahim (2012) using squared error loss function. The Bayesian estimate of the scale parameter of the Exponential distribution is obtained by making use of Lindley’s approximation procedure and compared with the classical maximum likelihood estimator. Mean Squared Error (MSE) and the absolute bias of the estimators are determined via simulation study for the purpose of comparison. It has been observed from the simulation study that, Bayes estimator with the generalised non- informative prior outperformed the gamma non-informative prior and the classical maximum likelihood estimator.
Highlights
Exponential distribution is the most exploited distribution for life-time data analysis
Its suitability is restricted to a constant hazard rate, which is difficult to justify in many practical problems
In this study we present and compare Bayes estimator using gamma and generalised non-informative priors for the estimation of the exponential scale parameter with the squared error loss function against the classical maximum likelihood estimator
Summary
Exponential distribution is the most exploited distribution for life-time data analysis. Guure et al (2012a) studied Bayesian estimation of two-parameter Weibull distribution using extension of Jeffreys' prior information with three loss functions. The extension of Jeffery prior information with new loss function for estimating the parameter exponential distribution of life time is presented by Alkutubi and Ibrahim (2009). In this study we present and compare Bayes estimator using gamma and generalised non-informative priors for the estimation of the exponential scale parameter with the squared error loss function against the classical maximum likelihood estimator. Generalised non-informative prior: According to Guure and Ibrahim (2012), the generalised noninformative prior is solely data dependent and is given with respect to the scale parameter of the exponential distribution as:. The exponential parameter is estimated with maximum likelihood and Bayesian using gamma non-informative prior and generalised noninformative prior approach. The mean squared error and absolute bias are given respectively as: R
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