  In this paper, we revisit the classical goodness-of-fit problems for
univariate distributions; we propose a new testing procedure based on a
characterisation of the uniform distribution. Asymptotic theory for the simple
hypothesis case is provided in a Hilbert-Space setting, including the
asymptotic null distribution as well as values for the first four cumulants of
this distribution, which are used to fit a Pearson system of distributions as
an approximation to the limit distribution. Numerical results indicate that the
null distribution of the test converges quickly to its asymptotic distribution,
making the critical values obtained using the Pearson system particularly
useful. Consistency of the test is shown against any fixed alternative
distribution and we derive the limiting behaviour under fixed alternatives with
an application to power approximation. We demonstrate the applicability of the
newly proposed test when testing composite hypotheses. A Monte Carlo power
study compares the finite sample power performance of the newly proposed test
to existing omnibus tests in both the simple and composite hypothesis settings.
This power study includes results related to testing for the uniform, normal
and Pareto distributions. The empirical results obtained indicate that the test
is competitive. An application of the newly proposed test in financial
modelling is also included.
