Table 1.
Simple statistics of y
| Mean | Std. Dev. | Coefficient of skewness | Coefficient of kurtosis | ||
|---|---|---|---|---|---|
| Log normal σ2=0.5 | 1.000 | 0.827 | 1.615 | 5.890 | |
| Log normal σ2=1 | 1.000 | 1.200 | 2.070 | 7.684 | |
| Log normal σ2=1.5 | 1.000 | 1.524 | 2.368 | 9.017 | |
| Log normal σ2=2 | 1.000 | 1.813 | 2.585 | 10.057 | |
| n=25 | Gamma α=0.5 | 1.000 | 1.402 | 1.962 | 6.885 |
| Gamma α =1 | 1.000 | 1.022 | 1.544 | 5.400 | |
| Gamma α =2 | 1.000 | 0.760 | 1.247 | 4.565 | |
| Gamma α =4 | 1.000 | 0.576 | 1.040 | 4.051 | |
| Wiebull α=0.5 | 1.000 | 1.939 | 2.592 | 9.902 | |
| Wiebull α =1 | 1.000 | 1.028 | 1.565 | 5.488 | |
| Wiebull α =5 | 1.000 | 0.363 | 0.668 | 3.131 | |
| Log normal σ2=0.5 | 1.000 | 0.841 | 1.992 | 8.305 | |
| Log normal σ2=1 | 1.000 | 1.251 | 2.669 | 12.101 | |
| Log normal σ2=1.5 | 1.000 | 1.626 | 3.132 | 15.086 | |
| Log normal σ2=2 | 1.000 | 2.060 | 3.476 | 17.481 | |
| n=50 | Gamma α=0.5 | 1.000 | 1.433 | 2.350 | 9.558 |
| Gamma α =1 | 1.000 | 1.049 | 1.824 | 7.064 | |
| Gamma α =2 | 1.000 | 0.769 | 1.459 | 5.691 | |
| Gamma α =4 | 1.000 | 0.579 | 1.192 | 4.788 | |
| Wiebull α=0.5 | 1.000 | 2.073 | 3.334 | 16.015 | |
| Wiebull α =1 | 1.000 | 1.047 | 1.846 | 7.182 | |
| Wiebull α =5 | 1.000 | 0.361 | 0.666 | 3.234 | |
| Log normal σ2=0.5 | 1.000 | 0.868 | 2.339 | 11.213 | |
| Log normal σ2=1 | 1.000 | 1.307 | 3.293 | 18.377 | |
| Log normal σ2=1.5 | 1.000 | 1.736 | 3.983 | 24.446 | |
| Log normal σ2=2 | 1.000 | 2.159 | 4.512 | 29.521 | |
| n=100 | Gamma α=0.5 | 1.000 | 1.466 | 2.681 | 12.454 |
| Gamma α =1 | 1.000 | 1.071 | 2.064 | 8.819 | |
| Gamma α =2 | 1.000 | 0.781 | 1.615 | 6.665 | |
| Gamma α =4 | 1.000 | 0.588 | 1.292 | 5.328 | |
| Wiebull α=0.5 | 1.000 | 2.178 | 4.095 | 24.487 | |
| Wiebull α =1 | 1.000 | 1.074 | 2.074 | 8.861 | |
| Wiebull α =5 | 1.000 | 0.370 | 0.626 | 3.054 | |
| Log normal σ2=0.5 | 1.000 | 0.888 | 2.892 | 18.063 | |
| Log normal σ2=1 | 1.000 | 1.364 | 4.667 | 40.650 | |
| Log normal σ2=1.5 | 1.000 | 1.880 | 6.206 | 65.574 | |
| Log normal σ2=2 | 1.000 | 2.420 | 7.508 | 89.605 | |
| n=500 | Gamma α=0.5 | 1.000 | 1.492 | 3.106 | 17.456 |
| Gamma α =1 | 1.000 | 1.076 | 2.320 | 11.267 | |
| Gamma α =2 | 1.000 | 0.789 | 1.764 | 7.819 | |
| Gamma α =4 | 1.000 | 0.594 | 1.369 | 5.826 | |
| Wiebull α=0.5 | 1.000 | 2.293 | 5.650 | 51.600 | |
| Wiebull α =1 | 1.000 | 1.077 | 2.317 | 11.208 | |
| Wiebull α =5 | 1.000 | 0.374 | 0.573 | 2.884 | |
| Log normal σ2=0.5 | 1.000 | 0.882 | 3.030 | 20.532 | |
| Log normal σ2=1 | 1.000 | 1.387 | 5.167 | 53.191 | |
| Log normal σ2=1.5 | 1.000 | 1.914 | 7.197 | 94.542 | |
| Log normal σ2=2 | 1.000 | 2.492 | 9.016 | 137.859 | |
| n=1000 | Gamma α=0.5 | 1.000 | 1.495 | 3.192 | 18.720 |
| Gamma α =1 | 1.000 | 1.078 | 2.367 | 11.805 | |
| Gamma α =2 | 1.000 | 0.791 | 1.786 | 8.018 | |
| Gamma α =4 | 1.000 | 0.597 | 1.381 | 5.909 | |
| Wiebull α=0.5 | 1.000 | 2.313 | 6.179 | 65.070 | |
| Wiebull α =1 | 1.000 | 1.078 | 2.360 | 11.684 | |
| Wiebull α =5 | 1.000 | 0.373 | 0.575 | 2.872 |