Exponential and related probability distributions on symmetric matrices

Abdelhamid Hassairi and Amel Roula

Statistics & Probability Letters, 2022, vol. 187, issue C

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.

Keywords: Exponential distribution; Uniform distribution; Pareto distribution; Helgason–Fourier transform; Reliability function (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109499

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