Fundamental Properties of the Characteristic Function using the Compound Poisson Distribution as the Sum of the Gamma Model

Authors

  • Meraou M. A. Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, Sidi Bel, Abbes 22000, Algeria Author
  • Noriah M. Al-Kandari Faculty of Science, Department of Statistics and Operations Research, Kuwait University, Al-Shedadiah, Kuwait Author
  • Raqab Z. Mohammad Department of Mathematics, The University of Jordan, Amman 11942, Jordan Author

DOI:

https://doi.org/10.64389/mjs.2025.01110

Keywords:

Compound Poisson, Characteristic function, Definite positive, Gamma variates, Quadratic form

Abstract

Probability distribution has proven its usefulness in almost every discipline of human endeavor. For this, the zero-truncated Poisson gamma (ZTP-G) model is widely recognized in probability theory and extensively used in various applied fields, specifically in survival, hydrology, insurance, and energy theory. The characterization of the zero-truncated Poisson sum of independent and identically distributed gamma random variables is proposed in this paper by applying the Laplace-Stieltjes transform technique. Further, the properties of continuity and quadratic form of the characteristic function are applied for definite positive properties from the ZTP-G model.

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Published

2025-07-11

Issue

Vol. 1 No. 1 (2025)

Section

Articles

License

Copyright (c) 2025 Meraou M. A., Noriah M. Al-Kandari, Raqab Z. Mohammad

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

M. A., M. ., Al-Kandari, N. M. ., & Mohammad, R. Z. . (2025). Fundamental Properties of the Characteristic Function using the Compound Poisson Distribution as the Sum of the Gamma Model. Modern Journal of Statistics, 1(1), 49-57. https://doi.org/10.64389/mjs.2025.01110