Antieigenvalues of Wishart Matrices

Abstract: In this thesis we derive the distribution for the first antieigenvalue for a random matrix with distribution W ∼ Wp(n, Ip) for p = 2 and p = 3. For p = 2 we present a proof that the first antieigenvalue has distribution β((n−1)/2, 1). For p = 3 we prove that the probability density function can be expressed using a sum of hypergeometric functions. Besides the main objective, the thesis seeks to introduce the theory of multivariate statistics and antieigenvalues.