A Simple Bayesian Estimation of the Gumbel Distribution

Practical use of Bayesian estimation of two-parameter Gumbel distribution often requires a two-dimensional joint prior distribution of the Gumbel parameters. It is particularly difficult to convince practitioners to believe any results from their subjective prior distribution. This paper obtains Bayesian estimation of two-parameter Gumbel distribution by using a simple Bayesian estimation procedure proposed by Kaminskiy and Vasiliy [4]. The prior information can be presented in the form of the interval assessment of the reliability function, which is generally easier to, obtain. Based on this prior information, the procedure allows constructing the continuous joint prior distribution of Gumbel parameters as well as the posterior estimates of the mean and standard deviation of the estimated reliability function (or the cumulative density function) at any given value of the exposure variable. A numeric example is discussed as an illustration.