DISTRIBUTION OF NONCENTRAL INDEFINITE QUADRATIC-FORMS IN COMPLEX NORMAL VARIABLES

A new series expansion is developed for the probability distribution f unction and the cumulative distribution function for indefinite noncen tral Hermitian quadratic forms in complex normal random variables, The moment generating function is inverted by contour integration using t he residue theorem, The function is separated into two parts, one part , containing an essential singularity, is expanded by Laurent series a nd the other part is expanded by Taylor series. The series are combine d for evaluating the residue of the complete function, Several differe nt series can be obtained by modifications of the basic approach, The series are computationally efficient and normally fast converging, The convergence rate depends on the separation of the eigenvalues, Multip le eigenvalues are allowed, and can be used to approximately replace a close pair of eigenvalues.