Research Article
Bayesian Estimation of Two-Parameter Weibull Distribution Using Extension of Jeffreys' Prior Information with Three Loss Functions
Table 4
Mean squared error for .
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| | 0.5 | 0.4 | 0.8 | 0.0219 | 0.0220 | 0.0211 | 0.0207 | 0.0212 | 0.0226 | 0.0192 | 0.0190 | 0.0240 | 0.0231 | | 0.5 | 0.4 | 1.2 | 0.0501 | 0.0516 | 0.0440 | 0.0459 | 0.0479 | 0.0492 | 0.0399 | 0.0429 | 0.0568 | 0.0515 | | 0.5 | 1.4 | 0.8 | 0.0229 | 0.0245 | 0.0209 | 0.0217 | 0.0230 | 0.0232 | 0.0196 | 0.0224 | 0.0253 | 0.0239 | 25 | 0.5 | 1.4 | 1.2 | 0.0488 | 0.0556 | 0.0509 | 0.0486 | 0.0549 | 0.0515 | 0.0439 | 0.0484 | 0.0597 | 0.0570 | 1.5 | 0.4 | 0.8 | 0.0228 | 0.0229 | 0.0198 | 0.0205 | 0.0214 | 0.0225 | 0.0196 | 0.0198 | 0.0228 | 0.0230 | | 1.5 | 0.4 | 1.2 | 0.0497 | 0.0511 | 0.0435 | 0.0445 | 0.0517 | 0.0487 | 0.0407 | 0.0421 | 0.0568 | 0.0491 | | 1.5 | 1.4 | 0.8 | 0.0233 | 0.0249 | 0.0220 | 0.0231 | 0.0241 | 0.0235 | 0.0199 | 0.0222 | 0.0241 | 0.0253 | | 1.5 | 1.4 | 1.2 | 0.0513 | 0.0584 | 0.0471 | 0.0515 | 0.0535 | 0.0545 | 0.0449 | 0.0486 | 0.0609 | 0.0587 |
| | 0.5 | 0.4 | 0.8 | 0.0094 | 0.0093 | 0.0089 | 0.0085 | 0.0089 | 0.0093 | 0.0086 | 0.0083 | 0.0095 | 0.0096 | | 0.5 | 0.4 | 1.2 | 0.0211 | 0.0213 | 0.0206 | 0.0200 | 0.0208 | 0.0204 | 0.0180 | 0.0202 | 0.0226 | 0.0207 | | 0.5 | 1.4 | 0.8 | 0.0095 | 0.0098 | 0.0092 | 0.0207 | 0.0099 | 0.0093 | 0.0089 | 0.0088 | 0.0098 | 0.0095 | 50 | 0.5 | 1.4 | 1.2 | 0.0209 | 0.0223 | 0.0206 | 0.0202 | 0.0215 | 0.0214 | 0.0201 | 0.0199 | 0.0235 | 0.0235 | 1.5 | 0.4 | 0.8 | 0.0094 | 0.0094 | 0.0088 | 0.0087 | 0.0092 | 0.0093 | 0.0088 | 0.0085 | 0.0094 | 0.0100 | | 1.5 | 0.4 | 1.2 | 0.0211 | 0.0213 | 0.0197 | 0.0197 | 0.0214 | 0.0205 | 0.0185 | 0.0188 | 0.0218 | 0.0216 | | 1.5 | 1.4 | 0.8 | 0.0091 | 0.0094 | 0.0095 | 0.0089 | 0.0093 | 0.0096 | 0.0087 | 0.0089 | 0.0218 | 0.0216 | | 1.5 | 1.4 | 1.2 | 0.0202 | 0.0215 | 0.0207 | 0.0201 | 0.0228 | 0.0224 | 0.0204 | 0.0198 | 0.0225 | 0.0224 |
| | 0.5 | 0.4 | 0.8 | 0.0042 | 0.0042 | 0.0041 | 0.0041 | 0.0041 | 0.0042 | 0.0041 | 0.0042 | 0.0043 | 0.0043 | | 0.5 | 0.4 | 1.2 | 0.0098 | 0.0099 | 0.0095 | 0.0092 | 0.0093 | 0.0097 | 0.0089 | 0.0091 | 0.0096 | 0.0099 | | 0.5 | 1.4 | 0.8 | 0.0042 | 0.0043 | 0.0042 | 0.0042 | 0.0042 | 0.0041 | 0.0042 | 0.0043 | 0.0044 | 0.0044 | 100 | 0.5 | 1.4 | 1.2 | 0.0096 | 0.0099 | 0.0096 | 0.0098 | 0.0097 | 0.0097 | 0.0091 | 0.0094 | 0.0101 | 0.0098 | 1.5 | 0.4 | 0.8 | 0.0044 | 0.0044 | 0.0042 | 0.0041 | 0.0042 | 0.0043 | 0.0042 | 0.0039 | 0.0042 | 0.0042 | | 1.5 | 0.4 | 1.2 | 0.0092 | 0.0093 | 0.0094 | 0.0096 | 0.0096 | 0.0095 | 0.0092 | 0.0090 | 0.0100 | 0.0098 | | 1.5 | 1.4 | 0.8 | 0.0043 | 0.0044 | 0.0042 | 0.0042 | 0.0042 | 0.0041 | 0.0039 | 0.0043 | 0.0043 | 0.0044 | | 1.5 | 1.4 | 1.2 | 0.0094 | 0.0097 | 0.0097 | 0.0095 | 0.0098 | 0.0097 | 0.0088 | 0.0093 | 0.0100 | 0.0095 |
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ML: maximum likelihood, BG: general entropy loss function, BL: LINEX loss function, BS: squared error loss function.
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