Abstract
Effective sample design has a major role in the quality of parameter estimation in statistical parameter estimation issues. The ranking set sampling (RSS) strategy is effective and a less costly option than simple random sampling (SRS). A novel mixture continuous lifetime distribution that has been proposed recently is the power Chris-Jerry distribution (PC-JD). It is useful for modeling a number of real data sets. This paper investigates the RSS approach for estimating the PC-JD's parameters. There are roughly sixteen different techniques of estimation that are used, such as the maximum likelihood method, the percentiles method, some methods based on minimum distance, the Kolmogorov method, and some methods based on minimum and maximum spacing distances. In comparison to a SRS, the simulation research assesses the performance of the suggested RSS-based estimates in terms of some measures of accuracy. To identify the optimal estimating strategy, the partial and overall ranks of many estimates are shown. According to numerical results, the maximum likelihood approach seems to be quite beneficial in evaluating the estimated quality of RSS and SRS. RSS is a more effective sampling approach than SRS owing to its better efficiency. Additionally, the different estimation techniques with survival data for both sampling techniques are examined.