SOME IMPROVED VARIANCE ESTIMATORS FROM A BIVARIATE NON-NORMAL POPULATION

Given paired observations, {(x(i), y(i)); i = 1, 2,...., n} on two variables x and y for a random sample s, from some bivariate non-normal population like bivariate gamma, beta-stacy which are of much use in modelling data obtained in Physical, Social and Life-Sciences. This paper considers an improvement of the customary estimator of population variance. A mixture (i.e. a weighted combination) of the customary estimator of the variance and a suitably chosen statistic t is proposed. It is also indicated that under some conditions for a broad range of the values of the mixing constants, the improvement in the sense of having a smaller mean square error, over the traditional estimator is possible.