We present an asymptotically parameter free and consistent goodness of fit test in the case of observations of Poisson processes. The basic hypothesis is supposed to be composite parametric. A statistic of Cramér-von Mises type with parameter replaced by the maximum likelihood estimator is proposed. We show that in the case of scale parameter, the distribution limit of the test statistic does not depend on the unknown parameter.

asymptotically parameter free test, Cramér-von Mises test, goodness of fit test, inhomogeneous Poisson process, parametric basic hypothesis.