5 papers · 1 filter
Algorithm for the product of Jack polynomials and its application to the sphericity test
Koki Shimizu, Hiroki Hashiguchi
In this study, we derive the density and distribution function of a ratio of the largest and smallest eigenvalues of a singular beta-Wishart matrix for the sphericity test. These f…
Generalized heterogeneous hypergeometric functions and the distribution of the largest eigenvalue of an elliptical Wishart matrix
Aya Shinozaki, Koki Shimizu, Hiroki Hashiguchi
In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions…
Approximation to probability density functions in sampling distributions based on Fourier cosine series
Shigekazu Nakagawa, Hiroki Hashiguchi, Yoko Ono
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions…
Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions
Koki Shimizu, Hiroki Hashiguchi
In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for multivariate analysis of variance (MANOVA) is discussed. The key to developing the d…
Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix
Koki Shimizu, Hiroki Hashiguchi
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statisti…