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Approximate distribution of eigenvalues of a generalized Wishart matrix under an extended Gaussian model

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  • Shimizu, Koki
  • Hashiguchi, Hiroki

Abstract

This paper discusses the distribution of the eigenvalues of a gamma matrix, which is generated from the product of an extended Gaussian matrix and its transposed matrix. We show that the distributions of the individual eigenvalues of a gamma matrix are approximated by the univariate gamma distribution when the first few eigenvalues of the scale parameter matrix are infinitely dispersed. Our results cover the eigenvalue distributions under the Gaussian and Kotz-type I models as special cases.

Suggested Citation

  • Shimizu, Koki & Hashiguchi, Hiroki, 2026. "Approximate distribution of eigenvalues of a generalized Wishart matrix under an extended Gaussian model," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s0167715225001804
    DOI: 10.1016/j.spl.2025.110535
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