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

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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 languageEnglish
Article number4343
Issue number20
StatePublished - Oct 2023
Externally publishedYes

Bibliographical note

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© 2023 by the author.


  • 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)

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