Improved estimation based on ranked set sampling for the Chris-Jerry distribution with application to engineering data

A less expensive and time-consuming option to simple random sampling (SRS) is the ranked set (RSS). Frequently, the RSS method produces more accurate estimators than those employed by SRS. The Chris-Jerry distribution (C-JD) is a new heavy-tailed distribution that helps model many data in human endeavors. The flexibility of the  C-JD  in capturing various hazard rate shapes ensures its applicability to a wide range of real-world data. This article’s primary objective is to examine how well fifteen different estimation techniques, such as maximum and minimum spacing distances methods, Kolmogorov method, and variations of the method of the minimum distances, perform when compared to the maximum likelihood method for parameter estimation of the C-JD based on RSS. We conduct comprehensive simulation research and assess the efficacy of various estimates based on RSS and SRS using many criterion measures. To identify the optimal estimating strategy, partial and overall ranks of the mean estimates, mean squared errors, maximum absolute differences, mean absolute relative errors, average absolute biases,  average absolute differences and average squared absolute error based on both designs are provided. The results of our study indicate that the maximum likelihood technique consistently outperforms other strategies, as evidenced by the overall rankings. Because RSS is more efficient than SRS, it is a more effective sampling method with lower accuracy measurements. To explain more, an actual data set about the fatigue life of a certain kind of Kevlar epoxy strand subjected to a constant continuous load at a pressure level of 90 % till the strand fails was examined.