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Some representations of the multivariate Bernoulli and binomial distributions

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  • Teugels, Jozef L

Abstract

Multivariate but vectorized versions for Bernoulli and binomial distributions are established using the concept of Kronecker product from matrix calculus. The multivariate Bernoulli distribution entails a parameterized model, that provides an alternative to the traditional log-linear model for binary variables.

Suggested Citation

  • Teugels, Jozef L, 1990. "Some representations of the multivariate Bernoulli and binomial distributions," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 256-268, February.
    • Handle: RePEc:eee:jmvana:v:32:y:1990:i:2:p:256-268
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    Cited by:

    1. Xiao,Tim, 2018. "Pricing Financial Derivatives Subject to Multilateral Credit Risk and Collateralization," EconStor Preprints 202075, ZBW - Leibniz Information Centre for Economics.
    2. White, Alan, 2018. "Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization," MPRA Paper 85331, University Library of Munich, Germany.
    3. Xiao, Tim, 2018. "The Valuation of Credit Default Swap with Counterparty Risk and Collateralization," EconStor Preprints 203447, ZBW - Leibniz Information Centre for Economics.
    4. Xiao, Tim, 2013. "The Impact of Default Dependency and Collateralization on Asset Pricing and Credit Risk Modeling," MPRA Paper 47136, University Library of Munich, Germany.
    5. Fontana, Roberto & Semeraro, Patrizia, 2018. "Representation of multivariate Bernoulli distributions with a given set of specified moments," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 290-303.
    6. Alberto Maydeu-Olivares & Rosa Montaño, 2013. "How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 116-133, January.
    7. Euán, Carolina & Sun, Ying, 2020. "Bernoulli vector autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    8. Lee, David, 2023. "Modeling Collateralization and Its Economic Significance," MPRA Paper 118678, University Library of Munich, Germany.
    9. Lieven Baele & Geert Bekaert & Koen Inghelbrecht & Min Wei, 2020. "Flights to Safety," The Review of Financial Studies, Society for Financial Studies, vol. 33(2), pages 689-746.
    10. Alan White, 2018. "Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization," Papers 1803.07843, arXiv.org.
    11. Ip, Edward H. & Wang, Yuchung J. & Yeh, Yeong-nan, 2004. "Structural decompositions of multivariate distributions with applications in moment and cumulant," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 119-134, April.
    12. Taylor, James W., 2017. "Probabilistic forecasting of wind power ramp events using autoregressive logit models," European Journal of Operational Research, Elsevier, vol. 259(2), pages 703-712.
    13. Zhigang Li & Katherine Lee & Margaret R. Karagas & Juliette C. Madan & Anne G. Hoen & A. James O’Malley & Hongzhe Li, 2018. "Conditional Regression Based on a Multivariate Zero-Inflated Logistic-Normal Model for Microbiome Relative Abundance Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 587-608, December.
    14. Albert Maydeu-Olivares & Harry Joe, 2006. "Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 713-732, December.
    15. Wu, Jianmin & Bentler, Peter M., 2013. "Limited information estimation in binary factor analysis: A review and extension," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 392-403.
    16. Wermuth, Nanny & Marchetti, Giovanni M. & Zwiernik, Piotr, 2014. "Binary distributions of concentric rings," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 252-260.
    17. Teugels, J. L. & Van Horebeek, J., 1998. "Algebraic Descriptions of Nominal Multivariate Discrete Data," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 203-226, November.
    18. Lovison, Gianfranco, 2006. "A matrix-valued Bernoulli distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1573-1585, August.
    19. Andrea Collevecchio & Robert Griffiths, 2023. "A Class of Non-Reversible Hypercube Long-Range Random Walks and Bernoulli Autoregression," Journal of Theoretical Probability, Springer, vol. 36(1), pages 623-645, March.
    20. Maydeu-Olivares, Albert, 2002. "Limited information estimation and testing of Thurstonian models for preference data," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 467-483, July.
    21. Tim, Xiao, 2019. "Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization," MPRA Paper 94701, University Library of Munich, Germany.
    22. Alan White, 2018. "Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization," Working Papers hal-01739310, HAL.
    23. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2022. "Stochastic representation of FGM copulas using multivariate Bernoulli random variables," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    24. Krause, Daniel & Scherer, Matthias & Schwinn, Jonas & Werner, Ralf, 2018. "Membership testing for Bernoulli and tail-dependence matrices," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 240-260.

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