On bivariate ranked set sampling for distribution and quantile estimation and quantile interval estimation using ratio estimator

As an extension to ranked set sampling (RSS), bivariate ranked set sampling (BVRSS) was introduced by Al-Saleh and Zheng [Al-Saleh, M. F., Zheng, G. (2002). Estimation of bivariate characteristics using ranked set sampling. Aust. New, Zealand J. Statist. 44:221-232] for multiple characteristics estimation. In this paper, BVRSS is investigated for estimating the joint and the marginal distribution functions using direct method of estimation. The estimation of a population quantiles of two characteristics based BVRSS, for given values of probability (p) using direct method of estimation, is investigated. Also, quantiles and quantiles intervals estimation, based on BVRSS, using ratio estimator is presented. It turns out that all the suggested estimators in this paper are more efficient than the corresponding estimators obtained by using bivariate SRS and the ordinary RSS with concomitant variable. Finally, the proposed methods are illustrated using real data set of the trees.