A review on concomitants of order statistics and its application in parameter estimation under ranked set sampling

The concomitants of order statistics (COS) is a variable associated with a bivariate sample when ordered with respect to the other variable. The distribution theory of COS is widely developed for various families of bivariate distributions. The COS have a wide variety of applications in different fields such as selection procedures, parameter estimation, ranked set sampling (RSS), etc. The notion of RSS in bivariate setup has been used to obtain improved estimates of parameters in many practical situations. Furthermore, many variations in the original idea of RSS have also been introduced. In this paper, we present a detail review of the families of bivariate distributions in view of the theory development of COS, the variations in RSS schemes and the use of RSS schemes in the estimation of parameters for different bivariate distributions. The shortfalls and advantages of RSS estimation are also summarised. The paper ends with some concluding remarks and possible future work in the area of RSS estimation.