Tail effect on maximal- t distribution. (a) The kernel smoothing density of the maximal-t statistics derived from 10,000 datasets drawn from the Pearson system (Eq.(2)) with skewness = 0 and various kurtosis. Each dataset contained 250 random numbers. (b) The smoothed probability density functions (PDFs) of the Pearson system with skewness = 0 and various kurtosis. The bottom of Figure 2b illustrates the heaviness of right tails for various kurtosis.