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A class of bivariate exponential distributions

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  • Regoli, Giuliana

Abstract

We introduce a class of absolutely continuous bivariate exponential distributions, generated from quadratic forms of standard multivariate normal variates. This class is quite flexible and tractable, since it is regulated by two parameters only, derived from the matrices of the quadratic forms: the correlation and the correlation of the squares of marginal components. A simple representation of the whole class is given in terms of 4-dimensional matrices. Integral forms allow evaluating the distribution function and the density function in most of the cases. The class is introduced as a subclass of bivariate distributions with chi-square marginals; bounds for the dimension of the generating normal variable are underlined in the general case. Finally, we sketch the extension to the multivariate case.

Suggested Citation

  • Regoli, Giuliana, 2009. "A class of bivariate exponential distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1261-1269, July.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1261-1269
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    References listed on IDEAS

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    1. V. Barnett, 1985. "The Bivariate Exponential Distribution; A Review And Some New Results," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 39(4), pages 343-356, December.
    2. Blacher, René, 2003. "Multivariate quadratic forms of random vectors," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 2-23, October.
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    Cited by:

    1. Tariq Saali & Mhamed Mesfioui & Ani Shabri, 2023. "Multivariate Extension of Raftery Copula," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    2. Muhammad Mohsin & Hannes Kazianka & Jürgen Pilz & Albrecht Gebhardt, 2014. "A new bivariate exponential distribution for modeling moderately negative dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 123-148, March.
    3. Li, Yang & Sun, Jianguo & Song, Shuguang, 2012. "Statistical analysis of bivariate failure time data with Marshall–Olkin Weibull models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2041-2050.

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