GS-distributions: A new family of distributions for continuous unimodal variables

  • Authors:

  • J. M. Muiño;E. O. Voit;A. Sorribas

  • Affiliations:

  • Departament de Ciències Mèdiques Bísiques, Universitat de Lleida, Avinguda Rovira Roure, 44, 25198-Lleida, Spain;The Wallace H. Coulter Department of Biomedical Engineering at Georgia Tech and Emory University, 313 Ferst Drive, Suite 4103 Atlanta, GA 30322, USA;Departament de Ciències Mèdiques Bísiques, Universitat de Lleida, Avinguda Rovira Roure, 44, 25198-Lleida, Spain

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2006

Quantified Score

Hi-index 0.03

Visualization

Abstract

The choice of the best-suited statistical distribution for modeling data is not a trivial issue. Unless a sound theoretical background exists for selecting a particular distribution, one will usually resort to testing various candidates and select a distribution based on its fit to the observed data. While this is a legitimate strategy, it is more objective and efficient to define a sufficiently general family that can be used for this purpose. This approach has a long tradition in statistics, and resulted in various families of distributions, most notably Pearson's. Given such a family, modeling a data set requires estimating the appropriate parameters within this family and assessing the resulting fit. As a contribution to this methodology, the Generalized S-distribution is introduced here as a new family of distributions that can serve as statistical models for unimodal continuous distributions. The article begins with a description of the rationale for defining this family. It then discusses its basic properties and introduces a numerical procedure for determining appropriate parameters using maximum likelihood estimation. Finally, the paper illustrates the distribution and methods with several examples.