Statistical Evaluation of Modality Test of Probability Density Function

• Activity Number: 110
• Type: Contributed
• Date/Time: Monday, August 3, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Mi-Chia Ma*+ and Hui-Ting Hsu
• Companies: National Cheng Kung University and National Cheng Kung University
• Keywords: Modality test ; Dip test ; Excess mass test ; Kolmogorov-Smirnov test ; Unimodal distribution ; Power

Abstract

Many methods were proposed to test the modality of probability density function in literatures, include the dip test, excess mass test and the calibrated excess mass test. Most of the test statistics of these methods were dependent on kernel density function estimate, so they were complicated and difficult on calculation. The Kolmogorov-Smirnov test is adjusted to test the modality. The spirit of this method is similar to the dip test. This method is straightforward and easy to compute and more convenient by current statistical package. A simulation study is conducted to compare these methods. The simulation results show that the power of adjusted Kolmogorov-Smirnov test is greater than that of the dip test for large sample size, and is competitive with that of the calibrated excess mass test when two modes are distant. Finally, a SNP data is illustrated to explain.