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 | \(\hat {\alpha }\) | 0.1885 | 0.1331 | 0.0237 | 0.0077 | 0.1246 | 0.2122 | 0.1316 | 0.0244 |
\(\hat {\rho }\) | 0.9471 | 0.9510 | 0.9668 | 0.9594 | 0.9803 | 0.9704 | 0.9754 | 0.9832 | |
\(\hat {s}\) | 0.0763 | 0.0457 | 0.0254 | 0.0191 | 0.0494 | 0.0383 | 0.0232 | 0.0132 | |
α= 0.05 | \(\hat {\alpha }\) | 0.1998 | 0.1447 | 0.0380 | 0.0208 | 0.1298 | 0.2221 | 0.1445 | 0.0421 |
\(\hat {\rho }\) | 0.9449 | 0.9481 | 0.9582 | 0.9495 | 0.9795 | 0.9692 | 0.9740 | 0.9791 | |
\(\hat {s}\) | 0.0776 | 0.0465 | 0.0271 | 0.0207 | 0.0504 | 0.0389 | 0.0236 | 0.0141 | |
α= 0.1 | \(\hat {\alpha }\) | 0.2129 | 0.1624 | 0.1027 | 0.1011 | 0.1365 | 0.2347 | 0.1622 | 0.0961 |
\(\hat {\rho }\) | 0.9418 | 0.9440 | 0.9411 | 0.9316 | 0.9783 | 0.9676 | 0.9719 | 0.9717 | |
\(\hat {s}\) | 0.0793 | 0.0475 | 0.0309 | 0.0241 | 0.0517 | 0.0397 | 0.0242 | 0.0158 | |
α= 0.2 | \(\hat {\alpha }\) | 0.2424 | 0.2123 | 0.1126 | 0.1220 | 0.1528 | 0.2639 | 0.2133 | 0.1179 |
\(\hat {\rho }\) | 0.9347 | 0.9335 | 0.9395 | 0.9290 | 0.9756 | 0.9637 | 0.9667 | 0.9694 | |
\(\hat {s}\) | 0.0830 | 0.0497 | 0.0314 | 0.0245 | 0.0545 | 0.0414 | 0.0254 | 0.0161 | |
ρ= 0.99 | ρ= 0.995 | ||||||||
α = 0.01 | \(\hat {\alpha }\) | 0.0154 | 0.0717 | 0.1503 | 0.2138 | 0.0046 | 0.0242 | 0.0737 | 0.1538 |
\(\hat {\rho }\) | 0.9990 | 0.9969 | 0.9950 | 0.9937 | 0.9998 | 0.9991 | 0.9983 | 0.9974 | |
\(\hat {s}\) | 0.0109 | 0.0134 | 0.0119 | 0.0091 | 0.0050 | 0.0075 | 0.0071 | 0.0061 | |
α= 0.05 | \(\hat {\alpha }\) | 0.0162 | 0.0753 | 0.1556 | 0.2239 | 0.0048 | 0.0253 | 0.0767 | 0.1583 |
\(\hat {\rho }\) | 0.9989 | 0.9968 | 0.9948 | 0.9935 | 0.9998 | 0.9991 | 0.9983 | 0.9973 | |
\(\hat {s}\) | 0.0112 | 0.0136 | 0.0121 | 0.0093 | 0.0051 | 0.0076 | 0.0073 | 0.0062 | |
α= 0.1 | \(\hat {\alpha }\) | 0.0168 | 0.0802 | 0.1647 | 0.2382 | 0.0054 | 0.0265 | 0.0801 | 0.1678 |
\(\hat {\rho }\) | 0.9989 | 0.9966 | 0.9945 | 0.9932 | 0.9997 | 0.9991 | 0.9982 | 0.9972 | |
\(\hat {s}\) | 0.0115 | 0.0140 | 0.0124 | 0.0095 | 0.0053 | 0.0078 | 0.0074 | 0.0064 | |
α= 0.2 | \(\hat {\alpha }\) | 0.0189 | 0.0887 | 0.1824 | 0.2728 | 0.0063 | 0.0303 | 0.0902 | 0.1849 |
\(\hat {\rho }\) | 0.9987 | 0.9962 | 0.9940 | 0.9924 | 0.9997 | 0.9989 | 0.9980 | 0.9969 | |
\(\hat {s}\) | 0.0123 | 0.0148 | 0.0128 | 0.0098 | 0.0056 | 0.0082 | 0.0076 | 0.0067 |