Basic Functions for Computational Implementation of the Box-Cox Symmetric Class of Distributions

Abstract

A class of distributions called Box-Cox symmetric was proposed for random variables with asymmetric distributions. This class allows through its structure an interpretation of the parameters in terms of quantiles (in particular, the median), relative dispersion and skewness. This study presents the initial results of the computational development of basic functions of each of the distributions that make up the Box-Cox symmetric class. Four functions have been developed to compose a routine in software R up to now. These functions are related to random numbers generation, probability density function, cumulative distribution function, and quantile function associated to a given probability. Examples of implemented functions were presented. The gamlss routine was used to check the performance of developed functions.