References
Goodman, N. R. (1963). Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction),Ann. Math. Statist.,34, 152–177.
Hayakawa, T. (1966). On the distribution of a quadratic form in a multivariate normal sample,Ann. Inst. Statist. Math.,18, 191–201.
Hayakawa, T. (1969). On the distribution of the latent roots of a positive definite random symmetric matrix I,Ann. Inst. Statist. Math.,21, 1–21.
Hayakawa, T. (1972). On the distribution of the latent roots of a complex Wishart matrix (Non-central case),Ann. Inst. Statist. Math.,24, 1–17.
Hayakawa, T. (1970). On the distribution of a trace of a multivariate quadratic form in the multivariate normal samples, Institute of Statist,Mimeo Series No. 682, University of North Carolina at Chapel Hill.
James, A. T. (1964). Distribution of matrix variates and latent roots derived from normal samples,Ann. Math. Statist.,35, 475–501.
Khatri, C. G. (1965). Classical statistical analysis based on a certain multivariate complex Gaussian distribution,Ann. Math. Statist.,36, 98–114.
Khatri, C. G. (1966). On certain distribution problems based on positive definite quadratic functions in normal vectors,Ann. Math. Statist.,37, 468–479.
Kotz, S., Johnson, N. L. and Boyd, D. W. (1967). Series representations of distributions of quadratic forms in normal variable II, Non-central case,Ann. Math. Statist.,38, 838–848.
Ruben, H. (1962). Probability content of regions under spherical normal distribution IV; the distribution of homogeneous and non-homogeneous quadratic functions of normal variables,Ann. Math. Statist.,33, 542–570.
Ruben, H. (1963). New results on the distribution of quadratic forms,Ann. Math. Statist.,34, 1582–1584.
Shah, B. H. (1970). Distribution theory of positive definite quadratic form with matrix argument,Ann. Math. Statist.,41, 692–697.
Brian G. Leach (1969). Bessel functions of matrix argument with statistical applications. (Thesis submitted for Ph.D. in University of Adelaide).
Additional information
This work was supported in part by the National Science Foundation under Grant No. GP 27715 (Indiana University), GU 2059 (University of North Carolina) and the Sakkokai Foundation.
The Institute of Statistical Mathematics
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Hayakawa, T. On the distribution of the multivariate quadratic form in multivariate normal samples. Ann Inst Stat Math 24, 205–230 (1972). https://doi.org/10.1007/BF02479752
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DOI: https://doi.org/10.1007/BF02479752