The traditional ranked set sampling (RSS) scheme can be viewed as an alternative to the simple random sampling (SRS) scheme in many lifetime scenarios. Over the years, numerous RSS-type methods have been proposed in the literature such as the ones with unequal sample sizes. This paper employs four sampling methods: the traditional RSS plan, two RSS-type plans with unequal sample sizes, and the SRS method to estimate the parameters of the exponentiated Shanker (E-Sh) distribution. The E-Sh distribution is particularly valuable for modeling lifetime phenomena due to its increasing or bathtub-shaped hazard rate function. Both classical and Bayesian frameworks are employed to derive point and interval estimates for the parameters. Since the Bayesian estimates seem to lack closed-form expressions, the Metropolis-Hastings within Gibbs algorithm is utilized to approximate these estimates. A simulation study is conducted to assess the performance of the different sampling strategies. The findings reveal that the traditional RSS method generally performs better than the others in classical estimation and Bayesian estimation under approximate non-informative priors. However, the RSS-type methods with unequal sample sizes prove competitive under Bayesian estimation with informative priors. A real data application involving diameter at breast height (DBH) data is also presented to illustrate the practical utility of the methods. The paper concludes with some final remarks.
Dehcheraghi et al. (Wed,) studied this question.