On general weighted extropy of percentile ranked set sampling

Extropy, introduced as a complementary measure to Shannon entropy, has recently received considerable attention in probability and statistics due to its ability to capture uncertainty from a perspective different from entropy. Several weighted and generalized versions of extropy have been proposed to incorporate the magnitude of the underlying random variable. In parallel, ranked set sampling and its variants have emerged as efficient alternatives to simple random sampling when ranking is inexpensive relative to exact measurement. In this paper, we develop a comprehensive study of the general weighted extropy (GWE) under the framework of Percentile Ranked Set Sampling (PRSS). Explicit expressions for the GWE of PRSS data are derived in terms of density–quantile functions, allowing tractable analysis. We investigate fundamental properties of the proposed measure, including monotonicity, stochastic ordering results, and bounds, and establish comparisons with the corresponding GWE under simple random sampling. The behavior of cumulative past extropy under PRSS is also examined. Furthermore, several characterization results are obtained, including characterizations of symmetric distributions and the exponential distribution based on the GWE of PRSS data. A Monte Carlo simulation study is conducted to compare the performance of extropy estimators based on PRSS, extreme ranked set sampling, and simple random sampling. The results demonstrate that PRSS-based estimators provide noticeable efficiency gains over their competitors in terms of mean squared error. Overall, the findings highlight the advantages of PRSS for uncertainty measurement and extend the theory of generalized weighted extropy to a flexible and practically relevant sampling scheme.