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LI Fei, XUE Yi-feng. Generalized Beta and F distributions of quaternion matrix argument (Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2010, (1): 85-90.
Citation:
LI Fei, XUE Yi-feng. Generalized Beta and F distributions of quaternion matrix argument (Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2010, (1): 85-90.
LI Fei, XUE Yi-feng. Generalized Beta and F distributions of quaternion matrix argument (Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2010, (1): 85-90.
Citation:
LI Fei, XUE Yi-feng. Generalized Beta and F distributions of quaternion matrix argument (Chinese)[J]. Journal of East China Normal University (Natural Sciences), 2010, (1): 85-90.
This paper computed the Jacobian of transformation textbfemphX=textbfemphBYB^mathrm T of singular quaternion matrices by using of the singular value decomposition of quaternion matrix and the density function of singular quaternion Wishart matrix. Then we defined the Beta and F distributions of quaternion matrix argument,and gave the density functions of the Beta and F distribution and the joint density functions of the nonzero eigenvalues of the singular quaternion matrices which satisfy the Beta or F distribution.