Generalized Chain Regression-cum-Chain Ratio Estimator for Population Mean under Stratified Extreme-cum-Median Ranked Set Sampling

Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under ranked set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized chain regression-cum-chain ratio type estimator to estimate finite population mean of study variable under stratified extreme-cum-median ranked set sampling utilizing information on two auxiliary variables. Mean square error (MSE) of the proposed generalized estimator is derived up to first order of approximation. The applications of the proposed estimator under symmetrical and asymmetrical probability distributions are discussed using simulation study and real-life data set for comparisons of efficiency. It is concluded that the proposed generalized estimator performs efficiently as compared to some existing estimators. It is also observed that the efficiency of the proposed estimator is directly proportional to the correlations between the study variable and its auxiliary variables.

A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods

In this manuscript, we investigate the estimation of the unknown reliability measure R = P [Y < X], in the case where Y and X are two independent random variables with Topp–Leone distributions. As the main contribution, various advanced sampling strategies are studied. The suggested strategies are simple random, ranked set, and median ranked set samplings. Firstly, based on the maximum likelihood, we give an efficient estimator of R when the observations of the two random variables are selected from the same simple random sample. Secondly, such an estimator is addressed when the observations of the two random variables are selected from the ranked set sampling method. Then, based on median ranked set sampling, the maximum likelihood estimator of R is addressed in all the four cases. When the observations from the two random variables are selected from the same set size, two cases are considered, while the other two cases are considered at different set sizes. A simulation research is developed to evaluate the behavior of the obtained estimates based on standard and median ranked set samplings with their simple random sampling equivalents. The ratio of mean square error is used to assess the effectiveness of these estimates.

Even Order Ranked Set Sampling with Auxiliary Variable

Even order ranked set sampling (EORSS) is a novel proposed ranked set sampling scheme connected with an auxiliary variable correlated with the study variable. This scheme quantifies only the one sampling unit which is at even position from each ranking set by employing specific criteria. The performance of the ratio estimator under EORSS is compared to its contemporary estimators in simple random sampling (SRS), ranked set sampling (RSS), median ranked set sampling (MRSS) and quartile ranked set sampling (QRSS) exploiting the same number of quantified units. The simulation results proved that EORSS is an efficient alternative sampling scheme for ratio estimation than SRS, RSS, MRSS and QRSS.