  In this paper, we consider the problem of deriving new eigenvalue
distributions of real-valued Wishart matrices that arises in many scientific
and engineering applications. The distributions are derived using the tools
from the theory of skew symmetric matrices. In particular, we relate the
multiple integrals of a determinant, which arises while finding the eigenvalue
distributions, in terms of the Pfaffian of skew-symmetric matrices. Pfaffians
being the square root of skew symmetric matrices are easy to compute than the
conventional distributions that involve Zonal polynomials or beta integrals. We
show that the plots of the derived distributions are exactly coinciding with
the numerically simulated plots.
