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 | \(\hat {\alpha }\) | 0.1671 | 0.0829 | 0.0565 | 0.0224 | 0.2399 | 0.1721 | 0.0847 | 0.0236 |
\(\hat {\rho }\) | 0.9291 | 0.9326 | 0.9291 | 0.9249 | 0.9507 | 0.9618 | 0.9629 | 0.9623 | |
\(\hat {s}\) | 0.1123 | 0.0236 | 0.0169 | 0.0111 | 0.1244 | 0.0199 | 0.0135 | 0.0065 | |
α= 0.05 | \(\hat {\alpha }\) | 0.2737 | 0.1658 | 0.1055 | 0.0567 | 0.3868 | 0.2383 | 0.1221 | 0.0582 |
\(\hat {\rho }\) | 0.9124 | 0.9231 | 0.9226 | 0.9197 | 0.9407 | 0.9561 | 0.9594 | 0.9597 | |
\(\hat {s}\) | 0.0964 | 0.0282 | 0.0190 | 0.0119 | 0.0972 | 0.0246 | 0.0155 | 0.0070 | |
α= 0.1 | \(\hat {\alpha }\) | 0.3461 | 0.2176 | 0.1430 | 0.0863 | 0.4543 | 0.2769 | 0.1545 | 0.0882 |
\(\hat {\rho }\) | 0.9044 | 0.9177 | 0.9188 | 0.9168 | 0.9355 | 0.9528 | 0.9574 | 0.9583 | |
\(\hat {s}\) | 0.0723 | 0.0307 | 0.0201 | 0.0123 | 0.0740 | 0.0271 | 0.0165 | 0.0073 | |
α= 0.2 | \(\hat {\alpha }\) | 0.4319 | 0.2836 | 0.2003 | 0.1414 | 0.5245 | 0.3257 | 0.2083 | 0.1424 |
\(\hat {\rho }\) | 0.8916 | 0.9109 | 0.9140 | 0.9132 | 0.9273 | 0.9488 | 0.9549 | 0.9564 | |
\(\hat {s}\) | 0.0714 | 0.0337 | 0.0214 | 0.0128 | 0.0638 | 0.0299 | 0.0176 | 0.0076 | |
ρ= 0.99 | ρ= 0.995 | ||||||||
α = 0.01 | \(\hat {\alpha }\) | 0.4342 | 0.2143 | 0.0862 | 0.0238 | 0.4681 | 0.2143 | 0.0862 | 0.0238 |
\(\hat {\rho }\) | 0.9698 | 0.9866 | 0.9904 | 0.9923 | 0.9728 | 0.9902 | 0.9941 | 0.9960 | |
\(\hat {s}\) | 0.1388 | 0.0174 | 0.0113 | 0.0037 | 0.1414 | 0.0162 | 0.0104 | 0.0034 | |
α= 0.05 | \(\hat {\alpha }\) | 0.5075 | 0.2529 | 0.1227 | 0.0585 | 0.5107 | 0.2529 | 0.1227 | 0.0585 |
\(\hat {\rho }\) | 0.9665 | 0.9841 | 0.9894 | 0.9917 | 0.9710 | 0.9883 | 0.9934 | 0.9958 | |
\(\hat {s}\) | 0.1011 | 0.0213 | 0.0129 | 0.0041 | 0.1006 | 0.0197 | 0.0118 | 0.0036 | |
α= 0.1 | \(\hat {\alpha }\) | 0.5329 | 0.2836 | 0.1547 | 0.0884 | 0.5349 | 0.2836 | 0.1547 | 0.0884 |
\(\hat {\rho }\) | 0.9650 | 0.9828 | 0.9889 | 0.9914 | 0.9701 | 0.9872 | 0.9931 | 0.9956 | |
\(\hat {s}\) | 0.0698 | 0.0233 | 0.0137 | 0.0042 | 0.0683 | 0.0215 | 0.0125 | 0.0038 | |
α= 0.2 | \(\hat {\alpha }\) | 0.5699 | 0.3286 | 0.2087 | 0.1426 | 0.5708 | 0.3286 | 0.2087 | 0.1426 |
\(\hat {\rho }\) | 0.9607 | 0.9812 | 0.9882 | 0.9911 | 0.9666 | 0.9860 | 0.9926 | 0.9954 | |
\(\hat {s}\) | 0.0561 | 0.0256 | 0.0146 | 0.0044 | 0.0534 | 0.0236 | 0.0134 | 0.0039 |