Table 4 MLE estimates for the parameters of \(\mathcal {EGW}\) distribution with Nelore data via BFGS, SANN, and Nelder–Mead algorithms
Methods | Parameters | Estimates | SE | Confidence Interval (0.95) |
|---|---|---|---|---|
BFGS | a | 0.01631688 | 0.004142414 | \(\left[ 0.01625805 ; 0.01637572 \right]\) |
b | 58.74132600 | 27.050302156 | \(\left[ 58.35713331 ; 59.12551870 \right]\) | |
\(\alpha\) | 0.03633065 | 0.004862259 | \(\left[ 0.03626159 ; 0.03639970 \right]\) | |
\(\beta\) | 3.17753052 | 0.241423958 | \(\left[ 3.17410160 ; 3.18095944 \right]\) | |
SANN | a | 0.801092593 | 0.495883447 | \(\left[ 0.794049611 ; 0.808135576 \right]\) |
b | 4.477365906 | 0.822148967 | \(\left[ 4.465689008 ; 4.489042804 \right]\) | |
\(\alpha\) | 0.009091301 | 0.002221628 | \(\left[ 0.009059748 ; 0.009122855 \right]\) | |
\(\beta\) | 2.454931581 | 0.286086581 | \(\left[ 2.450868322 ; 2.458994840 \right]\) | |
Nelder–Mead | a | 1.27972e−10 | – | – |
b | 13.08793619 | 4.6261741 | \(\left[ 13.0808279; 13.0950445\right]\) | |
\(\alpha\) | 0.69883693 | 0.2502418 | \(\left[ 0.6884190; 0.7092548\right]\) | |
\(\beta\) | 5.052449497 | 0.3667520 | \(\left[ 4.9210393; 5.1838597\right]\) |