Power Comparison of Some Goodness of Fit Tests

Abstract

Abstract There are some common goodness of fit tests that have been studied by researchers over the years such as the Shapiro-Wilk test, Anderson Darling test, Chi-square test and Bickel- Rosenblatt test. Researchers often use the goodness of fit test to decide if an underlying population distribution differs from a specific distribution. The main purpose of this thesis is to compare the power of some common goodness of fit tests, where a comparison of the proposed goodness of tests is conducted using the simulation method of sample data generated from some common distributions; R software was used to generate data by applying Monte Carlo simulation. The power of the tests generally affected by some factors like sample size and the type of distribution being tested in, however, the critical values are used for power comparisons that are obtained based on 10000 simulated samples from different distributions. The power of each test was then obtained by comparing the respective critical values with the goodness of fit test statistics. The main results based on the simulation study indicate that the Anderson Darling test has the highest power in the case of testing symmetric distributions when the data is generated from parametric alternative distributions, while the χ2 test has the lowest power. Furthermore, the Bickel-Rosenblatt test has the highest power in the case of testing symmetric distributions and the Anderson Darling test has the highest power under other non-parametric alternative distributions. This study also shows that when the Epanechnikov kernel is employed, the Bickel- Rosenblatt test has the highest power compared to the uniform kernel.