Symmetric Beta-Cauchy Distribution and Estimation of Parameters Using Order Statistics

Abstract

In this work, we have considered a class of distributions called symmetric beta-Cauchy family of distributions (SBCD), and pointed out instances where SBCD appears as a good model to study the stochastic nature of the variable under investigation. We have derived the Best linear unbiased estimators (BLUE) based on order statistics of the location and scale parameters of SBCD for some given values of the shape parameter. Considering these BLUE's as kernels of degree m(≤ 5), we have further estimated the location and scale parameters of SBCD by U-statistics as seen developed recently by Thomas and Sreekumar for any sample of size n. The exact variances of the U-statistics have been obtained. The efficiency of the obtained estimators relative to some of the standard estimators has been also evaluated. An illustration describing the supremacy of U-statistics estimation method over the classical maximum likelihood method is also given.