Let Q be a positive definite quadratic form of independent gamma random variables  with not necessarily identical shape parameters, which differs from a diagonal form only by a term proportional to  where Y is the sum of the  Then  is the corresponding quadratic form  of Dirichlet random variables. The exact cdf of  is given by a univariate integral over parabolic cylinder functions and by orthogonal series with Legendre or Jacobi polynomials. The cdf of Q is always available by an integral over the cdf of  and by a power series or a series of gamma cdfs. In the case of a diagonal form, the cdf is a convex combination of gamma cdfs. Finally, an integral representation for a general pos. def. quadratic form Q is derived, which is reduced to a double integral for a one-factorial quadratic form.

gamma distribution, Dirichlet distribution, exact distribution of quadratic forms of non-normal random variables, distribution of positive definite quadratic forms of gamma random variables, distribution of a positive definite diagonal quadratic form of Dirichlet random variables, test for the shape parameter of a gamma distribution, gamma coefficient of variation test.