A Cauchy-Quantile and Uniform Mixture Distribution Through the Method of Percentiles

• In Event: Application of Longitudinal Models and Statistical Theory

Abstract

This paper introduces a four-parameter probability distribution by mixing the quantile function of Cauchy distribution and its cumulative distribution function (cdf) represented by a uniform (0, 1) random variate using method of percentiles (MoP). Specifically, this proposed distribution is developed by mixing the Cauchy-quantile with a quadratic function of uniform (0, 1) random variate. Also presented in this paper is a MoP-based characterization of this distribution. Examples of fitting educational data are also presented. Monte Carlo simulation is used to demonstrate that the MoP-based estimates are substantially close to their respective parameters even for small sample sizes. One advantage of this distribution over other families of non-normal distributions is that it can fit data with negative values of skewness and/or kurtosis.

Author

• Mohan Dev Pant, Eastern Virginia Medical School