Tests of fit for the Rayleigh distribution
based
on the empirical
Simos G. Meintanis and George Iliopoulos
In this paper a class of goodness-of-fit tests for the Rayleigh distribution
with density $(2x/\theta^{2})\exp(-x^{2}/\theta^{2})$, $x\geq 0$, is proposed.
The tests are based on a weighted integral involving the empirical Laplace
transform. The consistency of the tests as well as their asymptotic
distribution under the null hypothesis are investigated. As the decay of the
weight function tends to infinity the test statistics approach limit values. In
a particular case the resulting limit statistic is related to the first nonzero
component of Neyman's smooth test for this distribution. The new tests are
compared with other omnibus tests for the Rayleigh distribution.
Key words and phrases: Rayleigh distribution, goodness-of-fit test,
empirical Laplace transform, smooth test.