Estimation of the Parameters of Bivariate Normal Distribution with Equal Coefficient of Variation Using Concomitants of Order Statistics

Abstract

To provide an optimum estimator for the parameters, the use of priori information has a crucial role in univariate as well as bivariate distributions. One such prior information is to utilize the knowledge on coefficient of variation in the inference problems. In the past plenty of work was carried out regarding the estimation of the mean $\mu$ of the normal distribution with known coefficient of variation. Also inference about the parameters of bivariate normal distribution in which $X$ and $Y$ have the equal (known) coefficient of variation $c$, are extensively discussed in the available literature. Such studies arise in clinical chemistry and pharmaceutical sciences. It is interesting to note that concomitants of order statistics are applied successfully to deal with statistical inference problems associated with several real life situations. A problem of interest considered here is the estimation of parameters of bivariate normal distribution in which $X$ and $Y$ have the same coefficient of variation $c$ using concomitants of order statistics. For that consider a sample of $n$ pairs of observations from a bivariate normal distribution in which $X$ and $Y$ have the same coefficient of variation $c$, we derive the best linear unbiased estimator (BLUE) of $\theta_2$ and derive some estimators of $\vartheta$. Efficiency comparisons are also made on the proposed estimators with some of the usual estimators, finally we conclude that efficiency of our best linear unbiased estimator (BLUE) $\tilde{\theta_{2}}$ is much better than that of the estimators $\hat{\theta}_{2}$ and $\theta^{\ast}_{2}$.