Articles

ON THE PROPERTIES OF SOME IMPORTANT DISTRIBUTIONS

Vol. 4 No. 53 (2026) 86-90

DOI: 10.5281/zenodo.20503693 2026-06-02 Articles CC BY 4.0 Open Access

Authors

  • Zuhriddin A. Nazarov Institute of Technology, Management and Communication, associate professor department of Mathematics and Informatics
  • Umidjon R. Rizoev Institute of Technology, Management and Communication, teacher department of Mathematics and Informatics,

Abstract

This paper provides a concise yet rigorous exposition of the negative binomial distribution, which generalizes the classical binomial model to accommodate overdispersion in count data. Owing to its derivation as a Poisson-Gamma mixture, the distribution possesses remarkable flexibility in modeling heterogeneous stochastic phenomena. It naturally arises in branching processes, risk theory and waiting time analysis.

Keywords:

negative binomial distribution stochastic processes Poisson and Gamma distributions parameter estimation.

References

Athreya K.B., Ney P.E. (2004). Branching Processes. Springer.

Kingman J.F.C. (1993). Poisson Processes. Oxford University Press.

Ars Conjectandi by Jacques Bernoulli, published posthumously in 1713.

Borovkov A.A.: Probability Theory. URSS, Moscow, 2009.

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Published

2026-06-02

Issue

Vol. 4 No. 53 (2026)

Section

Articles

License

Copyright (c) 2026 Innovative Academy RSC

Creative Commons License

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

How to Cite

Zuhriddin, A. N., & Umidjon, R. R. (2026). ON THE PROPERTIES OF SOME IMPORTANT DISTRIBUTIONS. Young Scientists, 4(53), 86-90. https://doi.org/10.5281/zenodo.20503693
Innovative Academy RSC
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