An improved method for estimating the parameters of the two-parameter cauchy distribution Conference

cited authors

  • Chen, Z; Zhu, A

fiu authors

abstract

  • The Cauchy distribution is a location-scale symmetric distribution with heavy tails. Estimating the parameters of the two-parameter Cauchy distribution is somewhat challenging because commonly used estimation methods cannot be used. In addition to the existing methods in the literature, a simple method for estimating the parameters of the location-scale distributions is proposed by Chen (2011). As a special case, the twoparameter Cauchy distribution was discussed in the paper. The method can provide decent estimation result in many cases. However, because of the wildness of the Cauchy distribution, the mean squared error of the point estimation of the parameters could be unacceptably large. The purpose of this paper is to find a modified approach for estimating the parameters of the two-parameter Cauchy distribution. It can be shown by Monte Carlo simulation that the MSE of the point estimation and the average length of the confidence intervals are greatly improved. It can also be shown that the estimators obtained in this paper are unbiased with respect to the median and possesses some optimal properties.

publication date

  • December 1, 2011

start page

  • 182

end page

  • 186