From: More efficient approaches to the exponentiated half-logistic distribution based on record values
\(\lambda \) | k | MSE(bias) | c | MSE(bias) | CI based on | |||
---|---|---|---|---|---|---|---|---|
\(\hat{\lambda }\) | \(\hat{\lambda }_p \left( \hat{\theta }_p \right) \) | \(\hat{\lambda }_B \left( \hat{\theta }_{MAP} \right) \) | \(\hat{\lambda }_{HB} \left( \hat{\theta }_{HMAP} \right) \) | \(\hat{\lambda }\) | \(W \left( \theta ^* \right) \) | |||
2 | 10 | 0.357 (0.239) | 0.175 (0.005) | 0.260 (0.115) | 5 | 0.170 (−0.003) | 0.977 | 0.954 |
100 | 0.173 (−0.004) | |||||||
500 | 0.173 (−0.004) | |||||||
12 | 0.230 (0.180) | 0.135 (0.003) | 0.179 (0.086) | 5 | 0.132 (−0.002) | 0.972 | 0.951 | |
100 | 0.135 (−0.002) | |||||||
500 | 0.135 (−0.002) | |||||||
14 | 0.151 (0.139) | 0.100 (−0.003) | 0.123 (0.065) | 5 | 0.099 (−0.002) | 0.971 | 0.949 | |
100 | 0.100 (−0.002) | |||||||
500 | 0.100 (−0.002) | |||||||
16 | 0.121 (0.119) | 0.085 (−0.003) | 0.101 (0.056) | 5 | 0.084 (−0.001) | 0.970 | 0.950 | |
100 | 0.085 (−0.001) | |||||||
500 | 0.085 (−0.001) | |||||||
4 | 10 | 0.771 (0.330) | 0.270 (0.020) | 0.427 (0.178) | 5 | 0.228 (−0.004) | 0.972 | 0.954 |
100 | 0.229 (−0.005) | |||||||
500 | 0.229 (−0.005) | |||||||
12 | 0.406 (0.230) | 0.189 (0.012) | 0.266 (0.126) | 5 | 0.172 (−0.005) | 0.968 | 0.951 | |
100 | 0.172 (−0.005) | |||||||
500 | 0.172 (−0.005) | |||||||
14 | 0.208 (0.167) | 0.120 (0.001) | 0.157 (0.089) | 5 | 0.115 (−0.003) | 0.968 | 0.950 | |
100 | 0.115 (−0.003) | |||||||
500 | 0.115 (−0.003) | |||||||
16 | 0.151 (0.136) | 0.096 (0.000) | 0.119 (0.072) | 5 | 0.094 (−0.002) | 0.966 | 0.949 | |
100 | 0.094 (−0.002) | |||||||
500 | 0.094 (−0.002) | |||||||
6 | 10 | 1.923 (0.454) | 0.468 (0.046) | 0.624 (0.227) | 5 | 0.294 (0.004) | 0.975 | 0.954 |
100 | 0.294 (0.004) | |||||||
500 | 0.294 (0.004) | |||||||
12 | 0.783 (0.298) | 0.289 (0.027) | 0.383 (0.159) | 5 | 0.224 (0.002) | 0.968 | 0.951 | |
100 | 0.224 (0.002) | |||||||
500 | 0.224 (0.002) | |||||||
14 | 0.306 (0.204) | 0.153 (0.008) | 0.208 (0.110) | 5 | 0.141 (−0.001) | 0.967 | 0.950 | |
100 | 0.141 (−0.001) | |||||||
500 | 0.141 (−0.001) | |||||||
16 | 0.195 (0.159) | 0.113 (0.003) | 0.146 (0.086) | 5 | 0.108 (−0.001) | 0.966 | 0.950 | |
100 | 0.108 (−0.001) | |||||||
500 | 0.108 (−0.001) | |||||||
8 | 10 | 5.376 (0.604) | 0.871 (0.079) | 0.769 (0.264) | 5 | 0.355 (0.009) | 0.975 | 0.952 |
100 | 0.355 (0.009) | |||||||
500 | 0.355 (0.009) | |||||||
12 | 1.522 (0.377) | 0.452 (0.047) | 0.488 (0.188) | 5 | 0.279 (0.006) | 0.967 | 0.951 | |
100 | 0.279 (0.006) | |||||||
500 | 0.279 (0.006) | |||||||
14 | 0.458 (0.247) | 0.202 (0.018) | 0.268 (0.130) | 5 | 0.171 (−0.003) | 0.964 | 0.950 | |
100 | 0.171 (−0.003) | |||||||
500 | 0.171 (−0.003) | |||||||
16 | 0.254 (0.186) | 0.134 (0.009) | 0.176 (0.099) | 5 | 0.124 (−0.003) | 0.962 | 0.950 | |
100 | 0.124 (−0.003) | |||||||
500 | 0.124 (−0.003) |