Abstract
This paper has investigated the estimation problem for the competing risks model where the data are adaptive progressively type-II censored and follow the Rayleigh distribution. Maximum likelihood and Bayesian methods are used to estimate the unknown parameters. To generate the interval estimates of the model parameters, approximate confidence intervals and two bootstrap confidence intervals are also considered based on the classical setup. Bayes estimates are obtained using independent gamma priors based on various loss functions including squared error, LINEX, general entropy, weighted SE, and precautionary loss functions. Moreover, Bayes credible intervals and the highest posterior density intervals of the model parameters are obtained. A numerical investigation has been carried out to assess the performance of the classical and Bayes estimates as well as the associated confidence and credible intervals. Finally, one simulated and two real data sets, one for breaking strengths of wire connections and the other for times to failure of small electrical appliances, have been analyzed for illustrative purposes. The results showed that the Bayes estimates using the LINEX loss function provide more reasonable estimates than the classical and Bayes estimates using squared error, general entropy, and precautionary loss functions.