Statistical Inference of Reliability Parameter for the Skew‐Normal Distribution under Progressive Type‐II Censored Samples

This study investigates the inference of the reliability parameter R = P[Y < X] for the skew-normal distribution based on progressively Type-II censored samples, where Y and X are two independent random variables. The maximum likelihood estimator and the asymptotic confidence interval for S = (2,2, …,2,5)1×20 are extracted via an iterative algorithm. Moreover, the Bayes estimator and the corresponding credible interval are computed using Gibbs sampling. Also, the MLE, UMVUE, Bayes estimator, and confidence interval are acquired when the scale parameter is known. We compare the performances of the different estimation methods using Monte Carlo simulations. Finally, the real datasets are analyzed for illustrative purposes.