Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions

In this paper, the exact distribution of largest eigenvalue a singular random matrix for multivariate analysis variance (MANOVA) is discussed. The key to developing theory eigenvalues use heterogeneous hypergeometric functions with two arguments. study, we define beta [Formula: see text]-matrix and extend distributions nonsingular case. We also give joint density in terms functions.