Estimation Of The Correlation Coefficient In Morgenstern Type Bivariate Exponential Distribution By Bivariate Ranked Set Sampling

When we do statistical inference work, we usually use simple random sampling to get sample from a population with unknown distribution. But in some real condition, it will take more time and effort to use simple random sampling. So we can use ranked set sampling. With ranked set sampling development so far, it appearred many achievement about parametric estimations, parametric hypotheses and nonparametric inference. Bivariate ranked set sampling was introduced by Al-Saleh(2002) as a bivariate version of ordinary ranked set sampling. The procedure can be used when we deal with two characteristics simultaneously. It is more efficient than bivariate simple random sample.In this article, we first introduce the background and sampling process of ranked set sampling, domestic and international research present condition about it. Then we introduce the concept and sampling steps of bivariate ranked set sampling, and the characters of sample density function. The main content is the unbiased estimation of the correlation coefficient in Morgenstem type bivariate exponential distribution by bivariate ranked set sampling, we discuss the estimation under the two cases that parameters λ, θ are known and unknown, compute the relative efficiency between bivariate ranked set sampling and bivariate simple random sampling. On that basis, we proved that it is more efficient by bivariate ranked set sampling than bivariate simple random sampling. Next we discuss the modified maximum likelihood estimation of the correlation coefficient in this condition and compare with the simple random sampling.Furthermore we proved the efficience of bivariate ranked set sampling. This article finally summarizes the already work.