Affiliation:
1. Department of Mathematics, Faculty of Sciences, Urmia University, Urmia, Iran
2. Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Guilan, Iran
Abstract
This study investigates the inference of the reliability parameter
for the skew-normal distribution based on progressively Type-II censored samples, where
and
are two independent random variables. The maximum likelihood estimator and the asymptotic confidence interval for
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.