Testing the validity of the logistic model based on the empirical distribution function

ABSTRACT

The logistic distribution is one of the fundamental distribution and is widely used for describing model growth curves in survival analysis and biological studies. Applications of this distribution are presented in statistical literature. In this article, goodness of fit tests for the logistic distribution based on the empirical distribution function (EDF) are considered. In order to compute the test statistics, because the MLEs cannot be obtained explicitly, we use the approximate maximum likelihood estimates (AMLEs) suggested by Balakrishnan and Cohen (1990), which are simple explicit estimators. Power comparisons of the considered tests are carried out via simulations. Finally, two illustrative examples are presented and analyzed.

KEYWORDS:

• Empirical distribution function
• Goodness of fit tests
• Logistic distribution
• Model validity
• Monte Carlo simulation
• Power study

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G10
• 62G30

Acknowledgments

The author is grateful to anonymous referees and the associate editor for providing some useful comments on an earlier version of this manuscript.