Nonnegative Unbiased Estimation of Scale Parameters and Associated Quantiles Based on a Ranked Set Sample

Abstract

In this article, we are interested in estimating the scale parameter in location and scale families. It is well known that the best linear unbiased estimator (BLUE) of scale parameter based on a simple random sample (SRS) is nonnegative. However, the BLUE of scale parameter based on a ranked set sample (RSS) can assume negative values. We suggest various modifications of BLUE of scale parameter based on RSS so that the resulting estimators are unbiased as well as nonnegative. Their performances in terms of relative efficiencies are compared and some recommendations are made for normal, logistic, double exponential, two-parameter exponential and Weibull distributions. We also briefly discuss an application of the proposed nonnegative BLUE of scale parameter for quantile estimation for the above populations.