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Exponential and related probability distributions on symmetric matrices

Author

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  • Hassairi, Abdelhamid
  • Roula, Amel

Abstract

Pursuing the study initiated in Hassairi and Roula (2019), we show in the present paper that the reliability function of a probability distribution on the cone Ω of positive definite symmetric matrices characterizes the distribution without any invariance condition. We also show that the characterization of the exponential probability distribution on Ω by a memoryless property holds without assuming an invariance condition. We then study the connection between the exponential distribution on Ω and the uniform distribution on a bounded interval of Ω. A notion of matrix Pareto distribution is introduced, and it is shown that this distribution possesses the long tail property.

Suggested Citation

  • Hassairi, Abdelhamid & Roula, Amel, 2022. "Exponential and related probability distributions on symmetric matrices," Statistics & Probability Letters, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:stapro:v:187:y:2022:i:c:s0167715222000815
    DOI: 10.1016/j.spl.2022.109499
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    References listed on IDEAS

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    1. Hassairi, A. & Roula, A., 2019. "Exponential probability distribution on symmetric matrices," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 37-42.
    2. A. Hassairi & S. Lajmi & R. Zine, 2008. "A Characterization of the Riesz Probability Distribution," Journal of Theoretical Probability, Springer, vol. 21(4), pages 773-790, December.
    3. Arjun K. Gupta & Daya K. Nagar, 2000. "Matrix-variate beta distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
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