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Moment for the inverse Riesz distributions

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  • Louati, Mahdi
  • Masmoudi, Afif

Abstract

The Riesz distributions dealing with positive definite symmetric matrices are usually used to introduce the class of the inverse Riesz distributions. The latter represents the natural extension of the class of the inverse Wishart. In this paper, we first present a sufficient condition allowing the existence of the expectation of the inverse Riesz distribution. Then, we compute it explicitly. For this purpose, we basically use the Cholesky decomposition as well as an important relation satisfied by the first derivative of continuous Riesz distribution’s density. The importance of this first moment consists in the fact that it can be used to estimate the shape parameter through the method of moments.

Suggested Citation

  • Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    • Handle: RePEc:eee:stapro:v:102:y:2015:i:c:p:30-37
    DOI: 10.1016/j.spl.2015.03.010
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    References listed on IDEAS

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    1. Kokonendji, Célestin C. & Khoudar, Mohamed, 2006. "On Lévy measures for infinitely divisible natural exponential families," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1364-1368, July.
    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. Andersson, Steen A. & Klein, Thomas, 2010. "On Riesz and Wishart distributions associated with decomposable undirected graphs," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 789-810, April.
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    Citations

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    Cited by:

    1. Abdelhamid Hassairi & Fatma Ktari & Raoudha Zine, 2022. "On the Gaussian representation of the Riesz probability distribution on symmetric matrices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 609-632, December.
    2. Andre Lucas & Anne Opschoor & Luca Rossini, 2021. "Tail Heterogeneity for Dynamic Covariance Matrices: the F-Riesz Distribution," Tinbergen Institute Discussion Papers 21-010/III, Tinbergen Institute, revised 11 Jul 2023.
    3. Kammoun, Kaouthar & Louati, Mahdi & Masmoudi, Afif, 2017. "Maximum likelihood estimator of the scale parameter for the Riesz distribution," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 127-131.
    4. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.
    5. Anne Opschoor & Dewi Peerlings & Luca Rossini & Andre Lucas, 2024. "Density Forecasting for Electricity Prices under Tail Heterogeneity with the t-Riesz Distribution," Tinbergen Institute Discussion Papers 24-049/III, Tinbergen Institute.

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