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.
| Original language | English |
|---|---|
| Article number | 4343 |
| Journal | Mathematics |
| Volume | 11 |
| Issue number | 20 |
| DOIs | |
| State | Published - Oct 2023 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2023 by the author.
Keywords
- Landau distribution
- characterizations
- exponential dispersion model
- exponential variance function
- generalized linear model
- natural exponential family
- self-decomposability
- unimodality
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- General Mathematics
- Engineering (miscellaneous)