Parameter Estimation of the Cauchy Distribution in Information Theory Approach

As we know the Cauchy distribution plays an important role in Probability Theory and Statistics. In this paper, we investigate the estimation of the location and the scale parameter. Both the one-dimensional problem and the multidimensional problem are studied for large sample. In the one-dimensional case, we give two algorithms for the estimation. The first one is an iterative method for which we prove the convergence and we show that the rate of convergence is geometric. The second algorithm provides an exact solution to the problem. In the multidimensional case, we give an algorithm analogous to the one-dimensional case. Computer experiments show that the rate of convergence is similar to the one-dimensional iterative algorithm.