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Duality between matrix variate t and matrix variate V.G. distributions

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  • Harrar, Solomon W.
  • Seneta, Eugene
  • Gupta, Arjun K.

Abstract

The (univariate) t-distribution and symmetric V.G. distribution are competing models [D.S. Madan, E. Seneta, The variance gamma (V.G.) model for share market returns, J. Business 63 (1990) 511-524; T.W. Epps, Pricing Derivative Securities, World Scientific, Singapore, 2000 (Section 9.4)] for the distribution of log-increments of the price of a financial asset. Both result from scale-mixing of the normal distribution. The analogous matrix variate distributions and their characteristic functions are derived in the sequel and are dual to each other in the sense of a simple Duality Theorem. This theorem can thus be used to yield the derivation of the characteristic function of the t-distribution and is the essence of the idea used by Dreier and Kotz [A note on the characteristic function of the t-distribution, Statist. Probab. Lett. 57 (2002) 221-224]. The present paper generalizes the univariate ideas in Section 6 of Seneta [Fitting the variance-gamma (VG) model to financial data, stochastic methods and their applications, Papers in Honour of Chris Heyde, Applied Probability Trust, Sheffield, J. Appl. Probab. (Special Volume) 41A (2004) 177-187] to the general matrix generalized inverse gaussian (MGIG) distribution.

Suggested Citation

  • Harrar, Solomon W. & Seneta, Eugene & Gupta, Arjun K., 2006. "Duality between matrix variate t and matrix variate V.G. distributions," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1467-1475, July.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1467-1475
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    References listed on IDEAS

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    1. Ronald W. Butler, 1998. "Generalized Inverse Gaussian Distributions and their Wishart Connections," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 69-75, March.
    2. T W Epps, 2000. "Pricing Derivative Securities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4415, August.
    3. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    4. Dreier, I. & Kotz, S., 2002. "A note on the characteristic function of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 221-224, April.
    5. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
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    Cited by:

    1. Fung, Thomas & Seneta, Eugene, 2010. "Extending the multivariate generalised t and generalised VG distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 154-164, January.
    2. Tounsi, Mariem & Zine, Raoudha, 2012. "The inverse Riesz probability distribution on symmetric matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 174-182.
    3. Kozubowski, Tomasz J. & Mazur, Stepan & Podgorski, Krysztof, 2022. "Matrix Variate Generalized Laplace Distributions," Working Papers 2022:7, Örebro University, School of Business.

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