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

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  • Shaul K. Bar-Lev

    (Faculty of Industrial Engineering and Technology Management, HIT-Holon Institute of Technology, 52 Golomb St., Holon 5810201, Israel)

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.

Suggested Citation

  • Shaul K. Bar-Lev, 2023. "The Exponential Dispersion Model Generated by the Landau Distribution—A Comprehensive Review and Further Developments," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4343-:d:1263061
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    References listed on IDEAS

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    1. M. Marucho & C. A. Garcia Canal & Huner Fanchiotti, 2006. "The Landau Distribution For Charged Particles Traversing Thin Films," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(10), pages 1461-1476.
    2. Shaul K. Bar-Lev & Abram M. Kagan, 2009. "Bivariate Distributions with Gaussian-Type Dependence Structure," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 38(16-17), pages 2669-2676, October.
    3. Shaul K. Bar-Lev & Apostolos Batsidis & Jochen Einbeck & Xu Liu & Panpan Ren, 2023. "Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    4. Bar-Lev, Shaul K. & Bshouty, Daoud & Letac, Gérard, 1992. "Natural exponential families and self-decomposability," Statistics & Probability Letters, Elsevier, vol. 13(2), pages 147-152, January.
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    Cited by:

    1. Shaul K. Bar-Lev & Xu Liu & Ad Ridder & Ziyu Xiang, 2024. "Generalized Linear Model (GLM) Applications for the Exponential Dispersion Model Generated by the Landau Distribution," Mathematics, MDPI, vol. 12(13), pages 1-21, June.
    2. Raydonal Ospina & Patrícia L. Espinheira & Leilo A. Arias & Cleber M. Xavier & Víctor Leiva & Cecilia Castro, 2024. "New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications," Mathematics, MDPI, vol. 12(20), pages 1-44, October.

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