The Gumbel distribution is one of the most popular widely used distributions in climate modeling. In this paper, we present exact confidence intervals (CI) and joint confidence regions (JCR) for the parameters of Gumbel distribution based on record data. Exact CI and JCR for the parameters of inverse Weibull distribution are also discussed. Three numerical examples with climate data are presented to illustrate the proposed methods. A simulation study is conducted to study the performance of the proposed CI and region.
