The Procedure for Selecting a Curve from the Johnson System by Percentile Matching and Maximum Likelihood and Least Squares Approaches in R

Abstract

It describes the implementation and application of a procedure in the R language designed to select a distribution curve from the Johnson system. In the proposed procedure, unlike the already implemented function from the SuppDists package, the selection of a family of curves and the estimation of parameters is carried out using the percentile method and a combination of maximum likelihood and least squares methods. The ability to set the initial values of the quantile vector of the standard normal distribution allows the user to select the curve more flexibly. In addition, the assessment of the quality of the selection can be performed visually, using graphs of density functions and distribution functions, as well as formalized with the application of Pearson's chi-squared agreement criterion.