Estimation Of A Scale Parameter Of Morgenstern Type Bivariate Exponential Distribution By Ranked Set Sampling

When we do statistical inference work, we know ranked set sampling is appli-cable when a set of sampling units can be ranked easily by a judgement method. But ranking is not recommendable when the judgement method is crude and is not accurate for ranking. In this case,we can use an auxiliary variable for ranking of set of sampling units. That is to say, we may prefer to order some auxiliary variable easily measurable and associated with the study variable rather than rank the units of the study variable with a crude judgement method, increasing the efficiency of estimator.Ranked set sampling using auxiliary variable is widely applied.In this article, we first introduce the concept and procedure of ranked set sam-pling using auxiliary variable, the concept of Morgenstern type bivariate exponen-tial distribution and some important conclusions. Then we introduce some research achievements of ranked set sampling using auxiliary variable, and the Best linear unbiased estimator of a scale parameter of Morgenstern type bivariate exponential distribution by ranked set sampling exploiting the maximum Fisher information. The main content is the maximum likelihood estimator of a scale parameter of Morgenstern type bivariate exponential distribution by ranked set sampling using auxiliary variable, we discuss three different modified maximum likelihood estima-tions:the modified maximum likelihood estimator of a scale parameter by balanced ranked set sampling method; the modified maximum likelihood estimator of a s-cale parameter by unbalanced ranked set sampling method exploiting the maximum Fisher information; the modified maximum likelihood estimator of a scale parameter by unbalanced multistage ranked set sampling method. Furthermore we conclude that the modified maximum likelihood estimator by unbalanced ranked set sam-pling method exploiting the maximum Fisher information is not only more effective than the modified maximum likelihood estimator by balanced ranked set sampling method, but it is also the Best linear unbiased estimator. This article finally sum-marizes the already work.