Table 2 shows the results of the Bayesian estimation of competing deterioration-hazard models for each of the databases ,
,
and original data set. The estimations obtained by the M-H method show the probability distribution of the parameters. In Table 2 the values estimated by the Bayesian estimation method are the sample average of parameters, and the values in parentheses refer to 95% credible intervals. All the credible intervals of estimated parameters do not contain zero. Because all the 95% confidence intervals do not contain zero, the estimated values will be significant at the 5% level (Wu & Hamada 2009). As shown in Table 2, as the amount of observation data increases the credible intervals become narrower. The absolute value of the Geweke test statistics shown in italic type are all less than 1.96, so the convergent hypothesis cannot be dismissed at a significance level of 5%.
Results of estimation of parameters for the competing deterioration-hazard model
| Parameters | D2000 | D5000 | D10000 | Original data set |
|---|---|---|---|---|
| −11.681 (−12.874, −10.617) | −9.955 (−10.717, −9.293) | −9.504 (−9.963, −9.055) | −9.594 (−9.941, −9.277) | |
| 0.053 | 0.086 | 0.036 | 0.069 | |
| −3.284 (−5.175, −1.165) | −2.929 (−4.369, −1.534) | −0.763 (−1.615, 0.047) | −0.994 (−1.595, −0.406) | |
| 0.134 | 0.035 | 0.060 | 0.011 | |
| 6.344 (1.065, 10.737) | 5.194 (2.239, 7.885) | 2.755 (1.412, 3.800) | 2.657 (1.941, 3.284) | |
| 0.042 | 0.129 | 0.124 | 0.038 | |
| −12.461 (−14.264, −10.842) | −10.332 (−11.358, −9.374) | −10.166 (−10.790, −9.644) | −10.094 (−10.429, −9.768) | |
| 0.139 | 0.200 | 0.067 | 0.226 | |
| −2.489 (−5.115, 0.287) | −3.100 (−5.468, −0.822) | −1.228 (−2.422, −0.189) | −1.884 (−2.863, −1.022) | |
| 0.391 | 0.354 | 0.197 | 0.112 | |
| 4.510 (−0.797, 7.570) | 8.126 (5.808, 10.720) | 3.396 (1.966, 4.409) | 3.106 (2.442,3.764) | |
| 0.303 | 0.036 | 0.145 | 0.001 | |
| 2.954 (2.600, 3.398) | 2.379 (2.178, 2.601) | 2.199 (2.051, 2.338) | 2.256 (2.161, 2.360) | |
| 0.090 | 0.120 | 0.032 | 0.070 | |
| 3.001 (2.528, 3.537) | 2.370 (2.078, 2.630) | 2.306 (2.147, 2.492) | 2.338 (2.237, 2.449) | |
| 0.083 | 0.105 | 0.003 | 0.188 |
| Parameters | D2000 | D5000 | D10000 | Original data set |
|---|---|---|---|---|
| −11.681 (−12.874, −10.617) | −9.955 (−10.717, −9.293) | −9.504 (−9.963, −9.055) | −9.594 (−9.941, −9.277) | |
| 0.053 | 0.086 | 0.036 | 0.069 | |
| −3.284 (−5.175, −1.165) | −2.929 (−4.369, −1.534) | −0.763 (−1.615, 0.047) | −0.994 (−1.595, −0.406) | |
| 0.134 | 0.035 | 0.060 | 0.011 | |
| 6.344 (1.065, 10.737) | 5.194 (2.239, 7.885) | 2.755 (1.412, 3.800) | 2.657 (1.941, 3.284) | |
| 0.042 | 0.129 | 0.124 | 0.038 | |
| −12.461 (−14.264, −10.842) | −10.332 (−11.358, −9.374) | −10.166 (−10.790, −9.644) | −10.094 (−10.429, −9.768) | |
| 0.139 | 0.200 | 0.067 | 0.226 | |
| −2.489 (−5.115, 0.287) | −3.100 (−5.468, −0.822) | −1.228 (−2.422, −0.189) | −1.884 (−2.863, −1.022) | |
| 0.391 | 0.354 | 0.197 | 0.112 | |
| 4.510 (−0.797, 7.570) | 8.126 (5.808, 10.720) | 3.396 (1.966, 4.409) | 3.106 (2.442,3.764) | |
| 0.303 | 0.036 | 0.145 | 0.001 | |
| 2.954 (2.600, 3.398) | 2.379 (2.178, 2.601) | 2.199 (2.051, 2.338) | 2.256 (2.161, 2.360) | |
| 0.090 | 0.120 | 0.032 | 0.070 | |
| 3.001 (2.528, 3.537) | 2.370 (2.078, 2.630) | 2.306 (2.147, 2.492) | 2.338 (2.237, 2.449) | |
| 0.083 | 0.105 | 0.003 | 0.188 |
Values in (·) show 95% credible intervals and values shown in italic type in each row are the Geweke statistical test.