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Bivariate Gamma Random Vectors

Author

Listed:
  • Bruce W. Schmeiser

    (Purdue University, West Lafayette, Indiana)

  • Ram Lal

    (California State University, Fullerton, California)

Abstract

A seven-parameter family of bivariate probability distributions is developed which allows for any gamma marginal distributions, any associated correlation (positive or negative), and a range of regression curves. The form of the family, which relies on the reproducibility property of the gamma distribution, is motivated by the search for tractable parameter estimation, general dependency structure, and straightforward computer sampling for simulation modeling. A modification with closed-form parameter estimation, but less general dependency structure, is also given. Finally, the use of these distributions in the form of first order autoregressive time series is discussed.

Suggested Citation

  • Bruce W. Schmeiser & Ram Lal, 1982. "Bivariate Gamma Random Vectors," Operations Research, INFORMS, vol. 30(2), pages 355-374, April.
    • Handle: RePEc:inm:oropre:v:30:y:1982:i:2:p:355-374
    DOI: 10.1287/opre.30.2.355
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    Cited by:

    1. Nurulkamal Masseran, 2021. "Modeling the Characteristics of Unhealthy Air Pollution Events: A Copula Approach," IJERPH, MDPI, vol. 18(16), pages 1-18, August.
    2. Hill, Raymond R. & Reilly, Charles H., 2000. "Multivariate composite distributions for coefficients in synthetic optimization problems," European Journal of Operational Research, Elsevier, vol. 121(1), pages 64-77, February.
    3. Higgins, Kevin, 2009. "Metapopulation extinction risk: Dispersal’s duplicity," Theoretical Population Biology, Elsevier, vol. 76(2), pages 146-155.
    4. Huifen Chen, 2001. "Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 312-331, November.
    5. Pan, Zhengqiang & Balakrishnan, Narayanaswamy, 2011. "Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 949-957.
    6. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    7. Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    8. Hüseyin Sarper, 2019. "Correlated reliability and an application: Propulsive landing on Mars," Journal of Risk and Reliability, , vol. 233(5), pages 826-846, October.
    9. Wheyming Tina, Song & Li-Ching, Hsiao & Yun-Ju, Chen, 1996. "Generating pseudo-random time series with specified marginal distributions," European Journal of Operational Research, Elsevier, vol. 94(1), pages 194-202, October.
    10. Stanhope, Stephen, 2005. "Case studies in multivariate-to-anything transforms for partially specified random vector generation," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 68-79, August.

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