The Effect of the Two Extremes in Estimating the Best Linear Unbiased Estimates (BLUE) of the Parameters of the Exponential Distribution

Several authors, [1], [2], [3], [4], [5], [6], [7], have considered linear estimation of the parameters of the exponential distribution from censored samples or by using selected order statistics. It was shown in [7] that missing the smallest observation in small samples from the two-parameter single exponential distribution greatly affects the efficiency of the BLUE of the location parameter. Moreover, this loss in efficiency depends upon the sample size. Insofar as the BLUE of the scale parameter is concerned, missing the largest observation in small samples results in a considerable loss of its efficiency. These empirical results were of considerable interest but the expressions for the loss of efficiencies due to missing one or both extremes in the oneand twoparameter exponential distributions were not derived. It is important to obtain such expressions in order to investigate such losses in relation to sample size. A comparison of the loss of information caused by missing the smallest and/or the largest observation will complete that part of the picture regarding estimation.