Convergence-guaranteed Independent Positive Semidefinite Tensor Analysis Based on Student's t Distribution

Chapter 7: Rectangular Matrix-Variate Distributions

“…where X and μ are 1 × q row vectors, the corresponding density in the complex domain, denoted by h( X), being the following: (7.5a.5) For specific values of the parameters, the densities appearing in (7.5.5) and (7.5a.5) can be respectively called the multivariate F and Student-t densities in the real and complex domains. With a view to model certain types of signal processes, (Kondo et al, 2020) made use of a special form of the complex multivariate Student-t wherein γ = 0, a = 2 ν and β = ν 2 , which is given next.…”

“…A complex multivariate Cauchy density that, as well, is mentioned in Kondo et al (2020), can be obtained by letting ν = 1 in (7.5a.6). We conclude this section with its representation, denoted by h2 ( X):…”