A Note on the Use of Some Functions of Spacings in the Estimation of Common Scale Parameter of Several Symmetric Distributions

In this article, we consider the problem of best linear unbiased estimation and best linear invariant estimation of the common scale parameter of several symmetric distributions using some functions of spacings of all observations taken from individual samples. We also proved a sufficient condition for the non negativity of the common scale estimator obtained by the above method. Furthermore, we obtained necessary and sufficient conditions for the derived estimators to be constant multiple of the sum of first and last spacings of the pooled sample.