Table 1 CP, AL, and tail error rates of all methods (\(\delta _1=\delta _2=0.1\), \(DL=0.1\)).
From: Confidence interval estimation for the difference of censored zero-inflated gamma distributions
\(DL=0.1\) | F | F-Li | F-Ren | F-Wilson | BC | BC-Li | BC-Ren | BC-Wilson | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\delta _1:\delta _2=0.1:0.1\) | CP | AL | CP | AL | CP | AL | CP | AL | CP | AL | CP | AL | CP | AL | CP | AL | |
\(n_1:n_2\) | \(a_1:a_2\) | \(ER_L\) | \(ER_R\) | \(ER_L\) | \(ER_R\) | \(ER_L\) | \(ER_R\) | \(ER_L\) | \(ER_R\) | \(ER_L\) | \(ER_R\) | \(ER_L\) | \(ER_R\) | \(ER_L\) | \(ER_R\) | \(ER_L\) | \(ER_R\) |
10:10 | 2:2 | 0.968 | 1.260 | 0.975 | 1.315 | 0.974 | 1.330 | 0.972 | 1.348 | 0.965 | 1.342 | 0.975 | 1.363 | 0.965 | 1.388 | 0.968 | 1.400 |
0.018 | 0.014 | 0.014 | 0.011 | 0.017 | 0.009 | 0.018 | 0.010 | 0.020 | 0.015 | 0.015 | 0.010 | 0.022 | 0.013 | 0.020 | 0.012 | ||
2:5 | 0.962 | 1.086 | 0.98 | 1.135 | 0.975 | 1.148 | 0.974 | 1.161 | 0.971 | 1.145 | 0.975 | 1.168 | 0.975 | 1.184 | 0.977 | 1.199 | |
0.010 | 0.028 | 0.004 | 0.016 | 0.010 | 0.015 | 0.009 | 0.017 | 0.009 | 0.020 | 0.003 | 0.022 | 0.007 | 0.018 | 0.007 | 0.016 | ||
5:5 | 0.949 | 0.871 | 0.971 | 0.918 | 0.961 | 0.928 | 0.961 | 0.938 | 0.956 | 0.897 | 0.975 | 0.912 | 0.959 | 0.925 | 0.967 | 0.938 | |
0.028 | 0.023 | 0.015 | 0.014 | 0.024 | 0.015 | 0.022 | 0.017 | 0.023 | 0.021 | 0.013 | 0.012 | 0.023 | 0.018 | 0.016 | 0.017 | ||
10:50 | 2:2 | 0.972 | 0.927 | 0.976 | 0.955 | 0.971 | 0.936 | 0.968 | 0.943 | 0.958 | 0.956 | 0.967 | 0.979 | 0.958 | 0.960 | 0.957 | 0.970 |
0.009 | 0.019 | 0.001 | 0.023 | 0.008 | 0.021 | 0.008 | 0.024 | 0.014 | 0.028 | 0.002 | 0.031 | 0.010 | 0.032 | 0.012 | 0.031 | ||
2:5 | 0.964 | 0.868 | 0.973 | 0.885 | 0.969 | 0.873 | 0.969 | 0.883 | 0.961 | 0.893 | 0.961 | 0.905 | 0.954 | 0.893 | 0.961 | 0.902 | |
0.006 | 0.030 | 0.001 | 0.027 | 0.006 | 0.025 | 0.006 | 0.025 | 0.009 | 0.030 | 0.002 | 0.037 | 0.009 | 0.036 | 0.009 | 0.030 | ||
5:5 | 0.964 | 0.623 | 0.977 | 0.643 | 0.964 | 0.632 | 0.963 | 0.637 | 0.966 | 0.624 | 0.977 | 0.637 | 0.969 | 0.625 | 0.969 | 0.633 | |
0.018 | 0.018 | 0.006 | 0.017 | 0.020 | 0.016 | 0.020 | 0.017 | 0.016 | 0.018 | 0.005 | 0.018 | 0.013 | 0.018 | 0.014 | 0.017 | ||
50:50 | 2:2 | 0.959 | 0.969 | 0.443 | 0.989 | 0.503 | 0.971 | 0.449 | 0.973 | 0.451 | 0.444 | 0.983 | 0.500 | 0.963 | 0.447 | 0.961 | 0.449 |
0.016 | 0.015 | 0.007 | 0.004 | 0.015 | 0.014 | 0.014 | 0.013 | 0.020 | 0.021 | 0.013 | 0.004 | 0.020 | 0.017 | 0.021 | 0.018 | ||
2:5 | 0.952 | 0.379 | 0.981 | 0.429 | 0.957 | 0.384 | 0.961 | 0.385 | 0.943 | 0.376 | 0.972 | 0.425 | 0.949 | 0.379 | 0.948 | 0.381 | |
0.012 | 0.036 | 0.001 | 0.018 | 0.013 | 0.030 | 0.012 | 0.027 | 0.015 | 0.042 | 0.003 | 0.025 | 0.016 | 0.035 | 0.016 | 0.036 | ||
5:5 | 0.952 | 0.295 | 0.977 | 0.333 | 0.955 | 0.301 | 0.956 | 0.302 | 0.947 | 0.294 | 0.979 | 0.328 | 0.952 | 0.295 | 0.952 | 0.296 | |
0.019 | 0.029 | 0.009 | 0.014 | 0.018 | 0.027 | 0.017 | 0.027 | 0.018 | 0.035 | 0.008 | 0.013 | 0.018 | 0.030 | 0.018 | 0.030 | ||
50:132 | 2:2 | 0.962 | 0.365 | 0.991 | 0.431 | 0.968 | 0.367 | 0.968 | 0.368 | 0.956 | 0.364 | 0.984 | 0.430 | 0.959 | 0.366 | 0.958 | 0.368 |
0.021 | 0.017 | 0.001 | 0.008 | 0.016 | 0.016 | 0.018 | 0.014 | 0.020 | 0.024 | 0.004 | 0.012 | 0.020 | 0.021 | 0.019 | 0.023 | ||
2:5 | 0.953 | 0.335 | 0.980 | 0.386 | 0.960 | 0.337 | 0.963 | 0.338 | 0.944 | 0.333 | 0.968 | 0.383 | 0.950 | 0.335 | 0.953 | 0.336 | |
0.013 | 0.034 | 0.001 | 0.019 | 0.012 | 0.028 | 0.012 | 0.025 | 0.014 | 0.042 | 0.002 | 0.030 | 0.014 | 0.036 | 0.013 | 0.034 | ||
5:5 | 0.955 | 0.241 | 0.981 | 0.283 | 0.956 | 0.244 | 0.957 | 0.244 | 0.956 | 0.240 | 0.978 | 0.280 | 0.952 | 0.241 | 0.955 | 0.241 | |
0.019 | 0.026 | 0.004 | 0.015 | 0.016 | 0.028 | 0.017 | 0.026 | 0.013 | 0.031 | 0.004 | 0.018 | 0.015 | 0.033 | 0.014 | 0.031 | ||
132:132 | 2:2 | 0.958 | 0.263 | 0.994 | 0.345 | 0.953 | 0.265 | 0.957 | 0.266 | 0.956 | 0.264 | 0.993 | 0.345 | 0.958 | 0.267 | 0.960 | 0.267 |
0.020 | 0.022 | 0.002 | 0.004 | 0.020 | 0.027 | 0.020 | 0.023 | 0.020 | 0.024 | 0.002 | 0.005 | 0.019 | 0.023 | 0.019 | 0.021 | ||
2:5 | 0.942 | 0.224 | 0.986 | 0.292 | 0.95 | 0.225 | 0.947 | 0.225 | 0.942 | 0.224 | 0.988 | 0.292 | 0.951 | 0.225 | 0.951 | 0.226 | |
0.012 | 0.046 | 0.001 | 0.013 | 0.012 | 0.038 | 0.011 | 0.042 | 0.014 | 0.044 | 0.001 | 0.011 | 0.011 | 0.038 | 0.011 | 0.038 | ||
5:5 | 0.940 | 0.174 | 0.992 | 0.225 | 0.942 | 0.175 | 0.944 | 0.176 | 0.948 | 0.174 | 0.990 | 0.224 | 0.943 | 0.174 | 0.936 | 0.175 | |
0.033 | 0.027 | 0.003 | 0.005 | 0.034 | 0.024 | 0.030 | 0.026 | 0.027 | 0.025 | 0.004 | 0.006 | 0.032 | 0.025 | 0.037 | 0.027 |