A Comparison of the Efficiency of Correlation Coefficient Tests for Mixture Distribution
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Abstract
This study aimed to compare the effectiveness of three correlation coefficient tests: the Pearson correlation coefficient test, the Spearman correlation coefficient test, and the Kendall tau correlation coefficient test. Three types of mixture distribution were considered: mixed normal, mixed log-normal, and mixed gamma. These distributions were the distribution of daily life data, such as rainfall, car insurance claim, etc. The sample sizes in this study were 10, 20, 30, 50, and 100. The correlation coefficients were 0.0, 0.4, 0.6, and 0.8, respectively. The results indicated that all tests could control type I error in all cases. For the power of the test in case of small sample size,The Pearson correlation coefficient test showed the greatest power. In case of a large sample size, this test also performed well for mixed normal distribution but for mixed log-normal and mixed gamma distributions, Kendall tau correlation coefficient test was the best.
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