The Exponential Dispersion Model Generated by the Landau Distribution—A Comprehensive Review and Further Developments

Abstract

The paper comprehensively studies the natural exponential family and its associated exponential dispersion model generated by the Landau distribution. These families exhibit probabilistic and statistical properties and are suitable for modeling skewed continuous data sets on the whole real line. The study explores and further develops various probabilistic properties, including reciprocity, self-decomposability, reproducibility, unimodality, and characterizations. It delves into statistical aspects such as maximum-likelihood estimation, hypothesis testing, and generalized linear models.

Keywords

• Landau distribution
• natural exponential family
• exponential dispersion model
• generalized linear model
• exponential variance function
• self-decomposability