Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 2, 306--326

Goodness-of-fit Tests For The Logistic Distribution Based on Empirical Transforms

Simos G. Meintanis ,  National and Kapodistrian University of Athens, Greece

SUMMARY. In this paper goodness-of-fit tests for the logistic distribution are proposed that are based on weighted integrals involving empirical transforms. The consistency of the test based on the empirical characteristic function as well as its asymptotic distribution under the null hypothesis are investigated. In a particular case, as the decay of the weight function tends to infinity the test statistic approaches a limit value. 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 logistic distribution.

AMS (1991) subject classification. 62G10, 62G20.

Key words and phrases. Logistic distribution, goodness-of-fit test, empirical characteristic function, empirical moment generating function, test. smooth.

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