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Table 2 Mean, variance, skewness and kurtosis calculations for GC(α, β,1)

From: The generalized Cauchy family of distributions with applications

α β Mean Variance Skewness Kurtosis
4 0.01 -10.7296 56.4986 -5.2367 *
  0.1 -0.8567 0.7824 -3.8549 *
  0.2 0.0774 0.6096 0.2118 *
  0.3 0.8738 2.7446 18.0382 *
5 0.01 -8.0673 21.2643 -3.4321 44.2181
  0.1 -0.5021 0.3953 -1.7868 17.6345
  0.2 0.4480 0.6855 2.4384 56.5459
  0.3 1.5732 6.8542 22.1028 *
8 0.01 -4.6280 3.5337 -1.9178 5.9542
  0.1 0.1248 0.2153 0.7560 3.2951
  0.2 1.6343 2.7528 6.3891 395.2955
  0.3 5.3887 124.9174 13.2288 *
10 0.01 -3.5986 1.6310 -1.5609 15.6352
  0.1 0.4431 0.2448 0.9704 8.1938
  0.2 2.7883 8.3416 8.3283 802.9949
  0.3 11.1914 840.3657 5.1306 *
  1. *Does not exist