Research Article
Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution
Table 3
Bias, MSE,
L, and CP of ML and Bayesian confidence interval based on GOS for Pareto distribution (
, and
).
| | | | OOS | FR | PTII | | | | | | |
| 0.148 | 10, 10 | | 0.077 | 0.148 | 0.116 | 0.049 | −0.022 | 0.158 | | 0.013 | 0.025 | 0.143 | 0.007 | 0.004 | 0.028 | | 0.352 | 0.390 | 0.614 | 0.348 | 0.395 | 0.391 | | 0.966 | 0.950 | 0.964 | 0.951 | 0.950 | 0.950 | 10, 15 | | 0.033 | 0.117 | −0.129 | 0.046 | −0.053 | 0.116 | | 0.006 | 0.015 | 0.026 | 0.006 | 0.005 | 0.015 | | 0.290 | 0.320 | 0.586 | 0.344 | 0.330 | 0.334 | | 0.959 | 0.950 | 0.954 | 0.950 | 0.950 | 0.950 | 15, 10 | | 0.146 | 0.166 | 0.700 | 0.031 | 0.037 | 0.188 | | 0.028 | 0.030 | 0.579 | 0.005 | 0.005 | 0.039 | | 0.215 | 0.318 | 0.525 | 0.333 | 0.313 | 0.324 | | 0.967 | 0.951 | 0.967 | 0.950 | 0.954 | 0.950 | 20, 20 | | 0.104 | 0.131 | −0.091 | −0.527 | 0.002 | 0.137 | | 0.014 | 0.018 | 0.134 | 0.282 | 0.002 | 0.020 | | 0.128 | 0.308 | 0.205 | 0.310 | 0.274 | 0.314 | | 0.975 | 0.950 | 0.914 | 0.950 | 0.975 | 0.950 |
| 0.83 | 10, 10 | | −0.078 | −0.421 | −0.097 | −0.525 | 0.020 | −0.153 | | 0.013 | 0.187 | 0.143 | 0.279 | 0.005 | 0.028 | | 0.841 | 0.549 | 0.577 | 0.376 | 0.502 | 0.726 | | 0.824 | 0.953 | 0.750 | 0.953 | 0.951 | 0.958 | 10, 15 | | −0.154 | −0.482 | −0.682 | −0.539 | −0.045 | −0.229 | | 0.031 | 0.237 | 0.551 | 0.293 | 0.006 | 0.059 | | 0.776 | 0.458 | 0.441 | 0.355 | 0.501 | 0.675 | | 0.952 | 0.951 | 0.941 | 0.952 | 0.913 | 0.957 | 15, 10 | | −0.033 | −0.413 | 0.155 | −0.520 | 0.060 | −0.137 | | 0.007 | 0.180 | 0.027 | 0.273 | 0.007 | 0.022 | | 0.760 | 0.446 | 0.424 | 0.355 | 0.419 | 0.632 | | 0.927 | 0.955 | 0.919 | 0.956 | 0.969 | 0.951 | 20, 20 | | −0.103 | −0.499 | 0.002 | −0.208 | −0.002 | −0.282 | | 0.014 | 0.251 | 0.171 | 0.047 | 0.002 | 0.085 | | 0.752 | 0.387 | 0.424 | 0.316 | 0.357 | 0.631 | | 0.897 | 0.951 | 0.942 | 0.953 | 0.953 | 0.954 |
| 0.5 | 10, 10 | | 0.003 | −0.103 | 0.017 | −0.205 | −0.005 | −0.008 | | 0.015 | 0.020 | 0.175 | 0.046 | 0.014 | 0.010 | | 0.644 | 0.535 | 0.319 | 0.379 | 0.645 | 0.620 | | 0.932 | 0.952 | 0.817 | 0.952 | 0.951 | 0.954 | 10, 15 | | −0.091 | −0.164 | −0.444 | −0.222 | −0.002 | −0.006 | | 0.020 | 0.031 | 0.232 | 0.053 | 0.015 | 0.012 | | 0.562 | 0.449 | 0.205 | 0.350 | 0.510 | 0.539 | | 0.885 | 0.958 | 0.962 | 0.957 | 0.785 | 0.956 | 15, 10 | | 0.087 | −0.085 | 0.446 | −0.192 | −0.124 | −0.098 | | 0.019 | 0.016 | 0.230 | 0.040 | 0.025 | 0.018 | | 0.514 | 0.446 | 0.202 | 0.349 | 0.435 | 0.486 | | 0.967 | 0.953 | 0.948 | 0.956 | 0.972 | 0.951 | 20, 20 | | −0.002 | −0.167 | 0.454 | −0.191 | −0.093 | −0.078 | | 0.006 | 0.029 | 0.233 | 0.040 | 0.016 | 0.016 | | 0.509 | 0.387 | 0.135 | 0.319 | 0.389 | 0.395 | | 0.959 | 0.952 | 0.933 | 0.952 | 0.943 | 0.951 |
|
|