The problem of estimating the parameters of a probability distribution from a sample is crucial to many fields of science and engineering, particularly for predicting future behavior of a phenomenon from previously observed behavior. A quantile regression offer a more complete statistical model than mean regression and has now widespread applications. In this article, we propose a method to estimate the parameters of continuous distributions using quantile regression through minimizing a data-based estimate of some appropriate quantile between the assumed model quantile and quantile underlying the data. The method is applicable when the quantile function is available in closed form. Also, the method is illustrated by estimate the parameters of normal and generalized extreme value distributions. |
