Table 1.
Comparison between Gaussian Hermite (GH) quadrature and proposed adaptive Gaussian Hermite (AGH)quadrature.
| Distribution | X ~ N(1, 2) | X ~ Exp(1) | ||||||
|---|---|---|---|---|---|---|---|---|
|
| ||||||||
| method | GH | AGH | GH | AGH | ||||
|
| ||||||||
| No of Nodes | E(X) | E(X2) | E(X) | E(X2) | E(X) | E(X2) | E(X) | E(X2) |
| 2 | 0.14 | 0.30 | 1.00 | 3.00 | 0.51 | 0.36 | 0.56 | 1.12 |
| 3 | 0.32 | 0.72 | 1.00 | 3.00 | 0.48 | 0.58 | 0.95 | 1.50 |
| 5 | 0.61 | 1.54 | 1.00 | 3.00 | 0.68 | 0.99 | 0.94 | 1.75 |
| 10 | 0.93 | 2.67 | 1.00 | 3.00 | 0.93 | 1.53 | 1.02 | 1.93 |
| 20 | 1.00 | 2.99 | 1.00 | 3.00 | 0.99 | 1.86 | 0.97 | 1.99 |
| 30 | 1.00 | 3.00 | 1.00 | 3.00 | 1.00 | 1.95 | 1.01 | 2.00 |
| true value | 1.00 | 3.00 | 1.00 | 3.00 | 1.00 | 2.00 | 1.00 | 2.00 |