Statistical inference on Gumbel distribution using record values

In this study, we address inference problems for Gumbel distribution when the available data are lower record values. We first derive unbiased estimators of unknown parameters, and then, we construct an exact confidence interval for the scale parameter and a predictive interval for the next lower value by deriving certain properties and pivotal quantities. These are compared with the results for existing inference. For Bayesian inference, we derive noninformative priors such as the Jeffreys and reference priors for unknown parameters and examine whether they satisfy the probability matching criteria; then, we apply them to develop objective Bayesian analysis.