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On the convolution of the negative binomial random variables

Author

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  • Furman, Edward

Abstract

In this note we are concerned with the sums S=Y1+Y2+...+Yn, where every constituent follows the negative binomial distribution with arbitrary parameters. We derive the exact probability mass function and the cumulative probability function of S. We also show that one can relate to the distribution of S as a mixture negative binomial distribution.

Suggested Citation

  • Furman, Edward, 2007. "On the convolution of the negative binomial random variables," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 169-172, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:2:p:169-172
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    Cited by:

    1. Hyunjin Lee & Taesik Lee, 2021. "Demand modelling for emergency medical service system with multiple casualties cases: k-inflated mixture regression model," Flexible Services and Manufacturing Journal, Springer, vol. 33(4), pages 1090-1115, December.
    2. Patrick W. Schmidt, 2020. "Inference under Superspreading: Determinants of SARS-CoV-2 Transmission in Germany," Papers 2011.04002, arXiv.org.
    3. Ninh, Anh & Bao, Yunhong & McGibney, Daniel & Nguyen, Tuan, 2024. "Clinical site selection problems with probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 316(2), pages 779-791.
    4. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    5. Mi, J. & Shi, W. & Zhou, Y.Y., 2008. "Some properties of convolutions of Pascal and Erlang random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2378-2387, October.
    6. Baena-Mirabete, S. & Puig, P., 2020. "Computing probabilities of integer-valued random variables by recurrence relations," Statistics & Probability Letters, Elsevier, vol. 161(C).

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