On the matched pairs sign test using bivariate ranked set sampling: an application to environmental issues

The matched pairs sign test using bivariate ranked set sampling (BVRSS) is introduced and investigated. We show that this test is asymptotically more efficient than its counterpart sign test based on a bivariate simple random sample (BVSRS). The asymptotic null distribution and the efficiency of the test are derived. The Pitman asymptotic relative efficiency is used to compare the asymptotic performance of the matched pairs sign test using BVRSS versus using BVSRS. For small sample sizes, the bootstrap method is used to estimate P-values. Numerical comparisons are used to gain insight about the efficiency of the BVRSS sign test compared to the BVSRS sign test. Our numerical and theoretical results indicate that using BVRSS for the matched pairs sign test is substantially more efficient than using BVSRS. Illustration using palm trees data from sultanate of Oman is provided.Key words: Bootstrap method, bivariate ranked set sample, power of the test, P-value of the test, Pitman’s relative efficiency, sign test

On Inference of Overlapping Coefficients in Two Lomax Populations Using Different Sampling Methods

This paper investigates point and interval estimation for some well-known measures of overlap. Two types of sampling procedures, namely, Simple Random Sample and Ranked Set Sample from two Lomax populations with different shape parameters are considered. Simulation studies are conducted to get insight on the performance of the proposed estimators. Taylor series approximations as well as bootstrap method are used to construct confidence intervals for those measures