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 | \(\hat {\alpha }\) | 0.0089 | 0.0106 | 0.0088 | 0.0084 | 0.0094 | 0.0111 | 0.0090 | 0.0090 |
\(\hat {\rho }\) | 0.9970 | 0.9966 | 0.9968 | 0.9969 | 0.9980 | 0.9978 | 0.9978 | 0.9979 | |
\(\hat {s}\) | 0.0269 | 0.0277 | 0.0304 | 0.0297 | 0.0221 | 0.0219 | 0.0260 | 0.0248 | |
α= 0.05 | \(\hat {\alpha }\) | 0.0387 | 0.0411 | 0.0397 | 0.0385 | 0.0425 | 0.0440 | 0.0433 | 0.0426 |
\(\hat {\rho }\) | 0.9868 | 0.9858 | 0.9865 | 0.9867 | 0.9911 | 0.9903 | 0.9909 | 0.9910 | |
\(\hat {s}\) | 0.0563 | 0.0595 | 0.0581 | 0.0577 | 0.0457 | 0.0488 | 0.0480 | 0.0477 | |
α= 0.1 | \(\hat {\alpha }\) | 0.0731 | 0.0779 | 0.0743 | 0.0752 | 0.0782 | 0.0835 | 0.0807 | 0.0807 |
\(\hat {\rho }\) | 0.9752 | 0.9737 | 0.9748 | 0.9751 | 0.9831 | 0.9819 | 0.9828 | 0.9830 | |
\(\hat {s}\) | 0.0767 | 0.0804 | 0.0783 | 0.0777 | 0.0631 | 0.0666 | 0.0647 | 0.0643 | |
α= 0.2 | \(\hat {\alpha }\) | 0.1387 | 0.1471 | 0.1415 | 0.1386 | 0.1518 | 0.1581 | 0.1517 | 0.1490 |
\(\hat {\rho }\) | 0.9536 | 0.9516 | 0.9532 | 0.9536 | 0.9679 | 0.9662 | 0.9675 | 0.9679 | |
\(\hat {s}\) | 0.1032 | 0.1073 | 0.1049 | 0.1042 | 0.0861 | 0.0900 | 0.0876 | 0.0871 | |
ρ= 0.99 | ρ= 0.995 | ||||||||
α = 0.01 | \(\hat {\alpha }\) | 0.0110 | 0.0133 | 0.0116 | 0.0103 | 0.0119 | 0.0142 | 0.0121 | 0.0106 |
\(\hat {\rho }\) | 0.9989 | 0.9988 | 0.9987 | 0.9988 | 0.9991 | 0.9990 | 0.9989 | 0.9990 | |
\(\hat {s}\) | 0.0167 | 0.0151 | 0.0205 | 0.0186 | 0.0155 | 0.0134 | 0.0191 | 0.0169 | |
α= 0.05 | \(\hat {\alpha }\) | 0.0501 | 0.0520 | 0.0502 | 0.0506 | 0.0534 | 0.0549 | 0.0530 | 0.0539 |
\(\hat {\rho }\) | 0.9952 | 0.9946 | 0.9950 | 0.9951 | 0.9960 | 0.9955 | 0.9958 | 0.9959 | |
\(\hat {s}\) | 0.0330 | 0.0354 | 0.0362 | 0.0356 | 0.0299 | 0.0320 | 0.0333 | 0.0326 | |
α= 0.1 | \(\hat {\alpha }\) | 0.0940 | 0.0977 | 0.0936 | 0.0959 | 0.0994 | 0.1048 | 0.0991 | 0.1003 |
\(\hat {\rho }\) | 0.9907 | 0.9898 | 0.9905 | 0.9906 | 0.9923 | 0.9915 | 0.9921 | 0.9922 | |
\(\hat {s}\) | 0.0458 | 0.0491 | 0.0481 | 0.0479 | 0.0414 | 0.0447 | 0.0441 | 0.0437 | |
α= 0.2 | \(\hat {\alpha }\) | 0.1774 | 0.1800 | 0.1755 | 0.1745 | 0.1878 | 0.1894 | 0.1852 | 0.1845 |
\(\hat {\rho }\) | 0.9821 | 0.9808 | 0.9818 | 0.9819 | 0.9850 | 0.9838 | 0.9847 | 0.9849 | |
\(\hat {s}\) | 0.0636 | 0.0674 | 0.0653 | 0.0651 | 0.0578 | 0.0615 | 0.0596 | 0.0595 |