Goodness-of-fit test for skew-t distribution

The skew-t distribution, characterized by skewness and heavy tails, has been widely applied in modeling financial, economic, and stock market data. In this article, we proposed several goodness-of-fit test methods designed for the skew-t distribution. These tests were grounded in probabilistic principles that establish connections between the skew-t distribution, the t distribution, and the F distribution. We achieved this by transforming random samples into approximate t-distributed and F-distributed variables. Subsequently, we introduced the Anderson-Darling (AD) test statistic and the sample correlation coefficient test for each variable transformation. Critical values for various sample sizes and significance levels were determined using the bootstrap method. To assess the effectiveness of our proposed methods, we compared the test power of these new tests with that of the classical Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) tests, performed before the variable transformation, across different sample sizes and under various alternative distributions. Simulation results indicated that the F-transform-based and classical untransformed AD tests generally performed competitively in terms of power against the considered alternative distributions.