Application of quantile methods to estimation of Cauchy distribution parameters

Abstract

Quantile methods are used for estimation of population parameters when other methods such as the maximum likelihood method and the method of moments cannot be applied. In the paper the percentile method, the quantile least squares method and its two modifications are considered. The proposed methods allow estimators to be obtained with smaller bias and smaller mean squared error than estimators of the quantile least squares method. The considered methods can be applied to estimation of the Cauchy distribution parameters. The results of the simulation analysis of the estimator properties have allowed conclusions to be drawn as concerning the application of the considered methods.