O-BLUE AND MINIMUM MSE LINEAR ESTIMATOR OF THE LOCATION PARAMETER OF AN EXPONENTIAL DISTRIBUTION WITH KNOWN COEFFICIENT OF VARIATION

We consider estimation of the location parameter of the exponential distribution having the pdf f(x) = (alpha theta)(-1) exp{-(x - theta)/alpha theta}, 0 <theta <= x< infinity, where. is unknown, a is positive and known. In this work we show that the O-BLUE estimator of. based on the available order statistics in type II censoring is identical to the minimum variance linear unbiased estimator constructed from the minimum variance unbiased estimators theta* and sigma* of the location and the scale parameters respectively in the full model. We also show that the minimum mean square error linear estimator of. based on the available order statistics is equivalent to the minimum mean square error linear estimator constructed from theta* and sigma*.