Bayesian Estimation, Prediction and Characterization for the Gumbel Model Based on Records

This is the authors' abstract. We don't add key points for this paper.

Bayesian estimation for the two parameters of the Gumbel distribution are obtained based on record values. Prediction, either point or interval, for future lower record values are also presented from a Bayesian view point. Some of the results of Ahsanullah (1991) can be obtained as limiting cases from our results. Based on a recurrence relation of conditional moments of nonadjacent record values, a characterization for the Gumbel distribution is also given. Numerical computations are given to illustrate these procedures.