Use of Quasi-Ranges in the Estimation of Scale Parameter of a Symmetric Distribution

Abstract

In this article, we consider the problem of best linear unbiased estimation and best linear invariant estimation of the scale parameter of a symmetric distribution using quasi-ranges is considered. We also prove a sufficient condition for the non negativity of the scale estimator obtained by the above method. Further, we obtain necessary and sufficient conditions for the derived estimators to be constant multiple of the sample range.

Characterization of Exponential Distribution Through Normalized Spacing of Generalized Order Statistics

“…[24] used the sample quasi range in setting confidence intervals for the population standard deviation. Further, [25] and [26] have used the sample quasi range in estimating the scale parameter for a location scale family of distribution, if the parent distribution is symmetric about the location parameter. Sample quasi range and range are also extensively used in quality control.…”