Application of Ranked Set Sampling in Parameter Estimation of Cambanis-Type Bivariate Exponential Distribution

Abstract

Ranked set sampling (RSS) is an efficient technique for estimating parameters and is applicable whenever ranking on a set of sampling units can be done easily by a judgment method or based on an auxiliary variable. In this paper, we assume (X,Y) to have a Cambanis-type bivariate exponential (CTBE) distribution, where a study variable Y is difficult and/or expensive to measure and is correlated with an auxiliary variable X that is readily measurable. The auxiliary variable is used to rank the sampling units. This paper addresses the problem of estimation of the scale parameter associated with the Y-variable based on the RSS scheme and some of the other modified RSS schemes. Comparison between estimators is done through relative efficiency to find the best RSS scheme. The efficiency performance of the estimators under various RSS schemes is presented numerically and graphically through 2-D and 3-D plots. To study the performance of the proposed estimators through a simulation study we develop a Matlab function to simulate data from the CTBE distribution. The results are applied to a real data set on mercury concentration in large mouth bass from Florida.

Keywords

• ranked set sampling
• concomitants of order statistics
• cambanis-type bivariate exponential distribution
• best linear unbiased estimators