A New Goodness-of-Fit Test: Free Chi-Square (FCS)

Abstract

This paper presents a new goodness-of-fit technique for testing the assumption of univariate distributions which is based on the theoretical distribution function of the hypothesized distribution. The existing methods are examined in two different categories: binning and binning-free. The most widely known binning test is the Chi-square test. The Kolmogorov-Smirnov, the Cramer-von Mises and the Anderson-Darling goodness-of-fit tests come to the forefront as the binning-free tests. When tests are evaluated in terms of distributions, it is examined in two different classes: the not distribution-free tests and the distribution-free tests. The desired goodness-of-fit test method for a researcher should be binning-free, distribution-free, more sensitivity, easy to use and fast. In this study, a test method is proposed which provides almost all the options that a researcher would want. The Monte-Carlo simulation methods are used to demonstrate the success of the proposed method. In these simulations, the normality test was applied for symmetric distributions whereas the lognormality test was applied for non-symmetric distributions. The proposed test method has demonstrated superiority in many aspects compared to other selected test methods on both simulations and three different real-life datasets.