From: Tolerance intervals in statistical software and robustness under model misspecification
n = 10 | n = 25 | n = 50 | n = 100 | n = 10 | n = 25 | n = 50 | n = 100 | ||
---|---|---|---|---|---|---|---|---|---|
ρ= 0.9 | ρ= 0.95 | ||||||||
α = 0.01 | \(\hat {\alpha }\) | 0.1824 | 0.1284 | 0.0617 | 0.0140 | 0.4086 | 0.3572 | 0.2632 | 0.1434 |
\(\hat {\rho }\) | 0.9399 | 0.9479 | 0.9578 | 0.9673 | 0.9495 | 0.9562 | 0.9646 | 0.9725 | |
\(\hat {s}\) | 0.0493 | 0.0405 | 0.0322 | 0.0244 | 0.0416 | 0.0341 | 0.0271 | 0.0205 | |
α= 0.05 | \(\hat {\alpha }\) | 0.2827 | 0.1771 | 0.0834 | 0.0195 | 0.5065 | 0.4151 | 0.2983 | 0.1658 |
\(\hat {\rho }\) | 0.9240 | 0.9411 | 0.9543 | 0.9655 | 0.9362 | 0.9505 | 0.9616 | 0.9710 | |
\(\hat {s}\) | 0.0618 | 0.0456 | 0.0349 | 0.0257 | 0.0523 | 0.0384 | 0.0293 | 0.0216 | |
α= 0.1 | \(\hat {\alpha }\) | 0.3370 | 0.2064 | 0.0966 | 0.0226 | 0.5579 | 0.4420 | 0.3163 | 0.1788 |
\(\hat {\rho }\) | 0.9149 | 0.9373 | 0.9523 | 0.9645 | 0.9285 | 0.9474 | 0.9600 | 0.9702 | |
\(\hat {s}\) | 0.0688 | 0.0484 | 0.0363 | 0.0264 | 0.0583 | 0.0408 | 0.0306 | 0.0222 | |
α= 0.2 | \(\hat {\alpha }\) | 0.3962 | 0.2406 | 0.1131 | 0.0276 | 0.6042 | 0.4736 | 0.3404 | 0.1909 |
\(\hat {\rho }\) | 0.9031 | 0.9326 | 0.9500 | 0.9633 | 0.9186 | 0.9434 | 0.9580 | 0.9692 | |
\(\hat {s}\) | 0.0776 | 0.0519 | 0.0381 | 0.0273 | 0.0660 | 0.0438 | 0.0321 | 0.0229 | |
ρ= 0.99 | ρ= 0.995 | ||||||||
α = 0.01 | \(\hat {\alpha }\) | 0.8260 | 0.8059 | 0.7660 | 0.7049 | 0.9058 | 0.8944 | 0.8733 | 0.8399 |
\(\hat {\rho }\) | 0.9616 | 0.9667 | 0.9730 | 0.9791 | 0.9647 | 0.9694 | 0.9753 | 0.9808 | |
\(\hat {s}\) | 0.0318 | 0.0260 | 0.0207 | 0.0156 | 0.0293 | 0.0239 | 0.0190 | 0.0143 | |
α= 0.05 | \(\hat {\alpha }\) | 0.8619 | 0.8272 | 0.7823 | 0.7201 | 0.9236 | 0.9064 | 0.8814 | 0.8484 |
\(\hat {\rho }\) | 0.9514 | 0.9624 | 0.9708 | 0.9780 | 0.9554 | 0.9655 | 0.9732 | 0.9798 | |
\(\hat {s}\) | 0.0401 | 0.0294 | 0.0224 | 0.0164 | 0.0369 | 0.0270 | 0.0206 | 0.0151 | |
α= 0.1 | \(\hat {\alpha }\) | 0.8781 | 0.8381 | 0.7921 | 0.7278 | 0.9303 | 0.9113 | 0.8864 | 0.8530 |
\(\hat {\rho }\) | 0.9455 | 0.9599 | 0.9696 | 0.9773 | 0.9500 | 0.9632 | 0.9721 | 0.9792 | |
\(\hat {s}\) | 0.0448 | 0.0312 | 0.0233 | 0.0169 | 0.0412 | 0.0287 | 0.0214 | 0.0155 | |
α= 0.2 | \(\hat {\alpha }\) | 0.8930 | 0.8499 | 0.8029 | 0.7355 | 0.9395 | 0.9173 | 0.8915 | 0.8572 |
\(\hat {\rho }\) | 0.9380 | 0.9569 | 0.9681 | 0.9766 | 0.9431 | 0.9605 | 0.9707 | 0.9785 | |
\(\hat {s}\) | 0.0508 | 0.0335 | 0.0245 | 0.0175 | 0.0468 | 0.0308 | 0.0225 | 0.0160 |