Inference for the Kumaraswamy distribution under k-record values

Based on the k-record values, inference is considered for the parameters of the Kumaraswamy distribution. The maximum likelihood estimates and alternative point estimates based on proposed pivotal quantities are provided for the unknown model parameters, and series of exact confidence intervals and exact confidence regions are constructed as well. For the confidence intervals and regions, the corresponding smallest-size confidence sets and their optimization procedures are presented based on minimizing the Lagrangian functions under given significance level. Two illustrative examples based on real and simulated data are provided to assess the performance of the proposed results.