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 | \(\hat {\alpha }\) | 0.0124 | 0.0096 | 0.0128 | 0.0112 | 0.0141 | 0.0115 | 0.0142 | 0.0140 |
\(\hat {\rho }\) | 0.9961 | 0.9963 | 0.9958 | 0.9957 | 0.9973 | 0.9974 | 0.9972 | 0.9970 | |
\(\hat {s}\) | 0.0277 | 0.0301 | 0.0291 | 0.0335 | 0.0222 | 0.0253 | 0.0234 | 0.0287 | |
α= 0.05 | \(\hat {\alpha }\) | 0.0483 | 0.0425 | 0.0498 | 0.0485 | 0.0557 | 0.0524 | 0.0607 | 0.0549 |
\(\hat {\rho }\) | 0.9837 | 0.9844 | 0.9824 | 0.9830 | 0.9885 | 0.9892 | 0.9877 | 0.9880 | |
\(\hat {s}\) | 0.0599 | 0.0587 | 0.0622 | 0.0634 | 0.0493 | 0.0488 | 0.0512 | 0.0531 | |
α= 0.1 | \(\hat {\alpha }\) | 0.0847 | 0.0834 | 0.0934 | 0.0853 | 0.0977 | 0.0973 | 0.1101 | 0.1023 |
\(\hat {\rho }\) | 0.9710 | 0.9715 | 0.9685 | 0.9699 | 0.9792 | 0.9799 | 0.9775 | 0.9784 | |
\(\hat {s}\) | 0.0804 | 0.0786 | 0.0838 | 0.0838 | 0.0672 | 0.0656 | 0.0698 | 0.0706 | |
α= 0.2 | \(\hat {\alpha }\) | 0.1519 | 0.1574 | 0.1652 | 0.1543 | 0.1768 | 0.1827 | 0.1901 | 0.1809 |
\(\hat {\rho }\) | 0.9490 | 0.9489 | 0.9452 | 0.9474 | 0.9630 | 0.9633 | 0.9600 | 0.9617 | |
\(\hat {s}\) | 0.1059 | 0.1044 | 0.1108 | 0.1094 | 0.0898 | 0.0879 | 0.0937 | 0.0933 | |
ρ= 0.99 | ρ= 0.995 | ||||||||
α = 0.01 | \(\hat {\alpha }\) | 0.0183 | 0.0166 | 0.0199 | 0.0180 | 0.0204 | 0.0182 | 0.0217 | 0.0199 |
\(\hat {\rho }\) | 0.9986 | 0.9985 | 0.9985 | 0.9982 | 0.9988 | 0.9987 | 0.9988 | 0.9984 | |
\(\hat {s}\) | 0.0158 | 0.0194 | 0.0166 | 0.0231 | 0.0142 | 0.0178 | 0.0149 | 0.0216 | |
α= 0.05 | \(\hat {\alpha }\) | 0.0738 | 0.0715 | 0.0832 | 0.0743 | 0.0820 | 0.0798 | 0.0901 | 0.0810 |
\(\hat {\rho }\) | 0.9933 | 0.9938 | 0.9930 | 0.9930 | 0.9944 | 0.9948 | 0.9941 | 0.9940 | |
\(\hat {s}\) | 0.0359 | 0.0367 | 0.0376 | 0.0407 | 0.0325 | 0.0337 | 0.0342 | 0.0376 | |
α= 0.1 | \(\hat {\alpha }\) | 0.1300 | 0.1326 | 0.1446 | 0.1360 | 0.1429 | 0.1469 | 0.1565 | 0.1507 |
\(\hat {\rho }\) | 0.9877 | 0.9884 | 0.9868 | 0.9872 | 0.9895 | 0.9902 | 0.9888 | 0.9891 | |
\(\hat {s}\) | 0.0501 | 0.0493 | 0.0521 | 0.0539 | 0.0456 | 0.0452 | 0.0476 | 0.0497 | |
α= 0.2 | \(\hat {\alpha }\) | 0.2334 | 0.2409 | 0.2451 | 0.2403 | 0.2520 | 0.2622 | 0.2669 | 0.2620 |
\(\hat {\rho }\) | 0.9775 | 0.9782 | 0.9757 | 0.9767 | 0.9807 | 0.9815 | 0.9792 | 0.9800 | |
\(\hat {s}\) | 0.0686 | 0.0667 | 0.0711 | 0.0720 | 0.0629 | 0.0612 | 0.0653 | 0.0664 |