Goodness-of-fit tests for the logistic distribution based on empirical transforms. (English) Zbl 1193.62080
Summary: Goodness-of-fit tests for the logistic distribution are proposed that are based on weighted integrals involving empirical transforms. The consistency of the tests based on the empirical characteristic function as well as their asymptotic distributions under the null hypothesis are investigated. In a particular case, as the decay of the weight function tends to infinity, the test statistics approach a limit value. The resulting limit statistics are related to the first non-zero component of Neyman’s smooth test for the distributions. The new tests are compared with other omnibus tests for logistic distributionsw.
MSC:
62G10 | Nonparametric hypothesis testing |
62G20 | Asymptotic properties of nonparametric inference |
62E20 | Asymptotic distribution theory in statistics |