GOODNESS-OF-FIT TESTS OF A PARAMETRIC DENSITY FUNCTIONS: MONTE CARLO SIMULATION STUDIES

Abstract

The purpose of this paper is to use Monte Carlo simulations to evaluate the
performance of six most popular statistics for testing the goodness of fit of a
parametric density function. The first three tests in this study are based on
the empirical distribution function which are simple and widely used. The other
three are based on directed and non-directional divergence measures and derived
from minimum relative entropy (MinxEnt) principle, m-spacing method and kernel
method. This study aims to evaluate the behavior of these tests by examining
the rejection rates under the hypothesis. It is shown that the tests based on the
directed divergence measure give a good approximation to the given significance
levels and are more powerful than other tests against the given alternative distributions.
It also suggests that the statistics based on the MinxEnt estimator
detect the distribution with higher kurtosis better than others.