Inference of stress-strength reliability fortwo-parameter of exponentiated gumbel distribution based on lower record values

Abstract

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This thesis investigates the estimation of the parameters of this distribution by using the lower record values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real datasets are provided to illustrate the proposed methods.