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Multivariate Generalized Beta Distributions with Applications to Utility Assessment

Author

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  • David L. Libby
  • Melvin R. Novick

Abstract

Two multivariate probability distributions, namely a generalized beta and a generalized F, that appear to be useful in utility modeling are derived. They reduce to the standard beta and F distributions, respectively, in special cases. Reproduction of distributional form is demonstrated for marginal and conditional distributions. Formulas for the moments of these distributions are given. The usefulness of these distributions in utility modeling derives from the fact that they generally do not demand increasing risk aversion as do most standard forms. An example of the use of the bivariate generalized beta distribution in utility modeling is presented. This distribution compares favorably in an example given here to both a normal model and an unstructured model.

Suggested Citation

  • David L. Libby & Melvin R. Novick, 1982. "Multivariate Generalized Beta Distributions with Applications to Utility Assessment," Journal of Educational and Behavioral Statistics, , vol. 7(4), pages 271-294, December.
    • Handle: RePEc:sae:jedbes:v:7:y:1982:i:4:p:271-294
    DOI: 10.3102/10769986007004271
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    Citations

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    Cited by:

    1. Arjun Gupta & Johanna Orozco-Castañeda & Daya Nagar, 2011. "Non-central bivariate beta distribution," Statistical Papers, Springer, vol. 52(1), pages 139-152, February.
    2. Kung-Yu Chen & Chien-Tai Lin, 2005. "A note on infinite-armed Bernoulli bandit problems with generalized beta prior distributions," Statistical Papers, Springer, vol. 46(1), pages 129-140, January.
    3. Saralees Nadarajah, 2006. "Sums, products and ratios of generalized beta variables," Statistical Papers, Springer, vol. 47(1), pages 69-90, January.
    4. A. El-Bassiouny & M. Jones, 2009. "A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 465-481, November.
    5. Olkin, Ingram & Trikalinos, Thomas A., 2015. "Constructions for a bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 54-60.
    6. Chu, J. & Nadarajah, S., 2018. "Estimating order statistics of network degrees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 869-885.
    7. Bai, Ray & Ghosh, Malay, 2018. "High-dimensional multivariate posterior consistency under global–local shrinkage priors," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 157-170.
    8. Krzysztof Kontek, 2010. "Maximum likelihood estimator for the uneven power distribution: application to DJI returns," Working Papers 43, Department of Applied Econometrics, Warsaw School of Economics.

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