Different Estimation Methods for the Unit Xgamma Distribution Using Ranked Set Sampling

Abstract

Ranked set sampling (RSS) is an efficient sampling method when ranking observations is easier than precise measurement. Unlike simple random sampling (SRS), RSS can reduce costs. The unit Xgamma distribution (UXGD), defined over the interval (0,1), effectively captures the characteristics of negatively skewed datasets. This study aims to comprehensively compare several estimation methods, including maximum likelihood, Anderson-Darling, Kolmogorov, ordinary least squares, Anderson-Darling left tail second order, Cramer-von-Mises, left tail Anderson-Darling, weighted least squares, maximum product spacing, right tail Anderson-Darling, and five types of minimum spacing distance for the UXGD parameter under both RSS and SRS techniques. Through extensive simulations, we evaluate the performance of these estimators using multiple criteria under both designs. We rank the estimators based on their performance under both sampling schemes. Simulation findings indicate that the maximum product spacing and maximum likelihood estimation methods are superior to alternative approaches for assessing the estimated quality of RSS and SRS, respectively. It is interesting to note that for both SRS and RSS datasets, the estimates revealed by our model satisfy the consistency property. With an increase in the sample size, the estimates approach the true parameter values. Furthermore, the results highlight the efficiency gains of RSS over SRS, as evidenced by improved accuracy metrics. Two real-world applications, including COVID-19 data from the United Kingdom and France, demonstrate the practical utility of our findings.