Efficient computation of Hoyt cumulative distribution function

A new expression for the cumulative distribution function (CDF) of the Hoyt (Nakagami-q) distribution is derived. Its evaluation requires only a single numerical integration and its form is particularly well-suited for numerical computation by a Gauss-Chebyshev quadrature (GCQ). This quadrature is analysed and an upper bound on the absolute error is given. As example results to demonstrate the GCQ method´s simplicity and efficiency, the computation of the Hoyt CDF and of the outage probability in Hoyt fading channels are presented.