We provide a new proof for the representation of Cramér-von Mises statistics under (known) gamma and normal distributions. The new method uses orthogonal polynomials and provides an explicit form of the statistics from which the asymptotic distribution can be calculated.
Keywords Cramér-von Mises family - goodness of fit - normal distribution - gamma distribution - orthogonal polynomials
Acknowledgements This research was partially supported by FQM-331, FQM-270, BMF 2001-2378 and BMF2002-04525-C02-02. The authors are thankful to the referees for their suggestions and helpful comments.