Research Article
Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution
Table 4
Bias, MSE,
L, and CP of ML and Bayesian confidence interval based on GOS for Pareto distribution (
, and
).
| | | | OOS | FR | PTII | | | | | | |
| 0.26 | 10, 10 | | 0.218 | 0.217 | 0.533 | 0.275 | 0.067 | 0.133 | | 0.064 | 0.051 | 0.392 | 0.085 | 0.014 | 0.021 | | 0.571 | 0.553 | 0.472 | 0.462 | 0.470 | 0.475 | | 0.964 | 0.950 | 0.879 | 0.955 | 0.968 | 0.953 | 10, 15 | | 0.157 | 0.195 | 0.018 | 0.274 | 0.003 | 0.113 | | 0.037 | 0.041 | 0.145 | 0.085 | 0.007 | 0.015 | | 0.559 | 0.527 | 0.432 | 0.461 | 0.376 | 0.431 | | 0.972 | 0.951 | 0.773 | 0.953 | 0.947 | 0.952 | 15, 10 | | 0.330 | 0.255 | 0.728 | 0.284 | 0.192 | 0.197 | | 0.120 | 0.067 | 0.532 | 0.091 | 0.045 | 0.042 | | 0.535 | 0.519 | 0.430 | 0.376 | 0.304 | 0.432 | | 0.951 | 0.950 | 0.871 | 0.952 | 0.961 | 0.950 | 20, 20 | | 0.283 | 0.237 | 0.327 | −0.053 | 0.143 | 0.200 | | 0.087 | 0.058 | 0.148 | 0.013 | 0.025 | 0.042 | | 0.444 | 0.436 | 0.430 | 0.320 | 0.293 | 0.316 | | 0.950 | 0.950 | 0.947 | 0.947 | 0.958 | 0.950 |
| 0.60 | 10, 10 | | 0.140 | −0.082 | 0.308 | −0.051 | 0.144 | −0.063 | | 0.031 | 0.009 | 0.147 | 0.013 | 0.030 | 0.007 | | 0.453 | 0.570 | 0.542 | 0.665 | 0.347 | 0.590 | | 0.975 | 0.952 | 0.835 | 0.958 | 0.972 | 0.951 | 10, 15 | | 0.079 | −0.101 | −0.101 | −0.046 | 0.046 | −0.090 | | 0.016 | 0.012 | 0.194 | 0.012 | 0.013 | 0.010 | | 0.382 | 0.543 | 0.386 | 0.663 | 0.324 | 0.552 | | 0.967 | 0.952 | 0.877 | 0.955 | 0.961 | 0.953 | 15, 10 | | 0.211 | −0.059 | 0.398 | −0.038 | 0.235 | −0.041 | | 0.051 | 0.005 | 0.159 | 0.011 | 0.060 | 0.004 | | 0.373 | 0.532 | 0.335 | 0.620 | 0.288 | 0.505 | | 0.959 | 0.955 | 0.880 | 0.950 | 0.951 | 0.954 | 20, 20 | | 0.163 | −0.087 | 0.089 | −0.317 | 0.182 | −0.070 | | 0.031 | 0.008 | 0.025 | 0.112 | 0.037 | 0.006 | | 0.317 | 0.532 | 0.326 | 0.552 | 0.230 | 0.456 | | 0.959 | 0.955 | 0.887 | 0.959 | 0.953 | 0.957 |
| 0.88 | 10, 10 | | 0.001 | −0.255 | 0.083 | −0.313 | 0.053 | −0.175 | | 0.003 | 0.069 | 0.026 | 0.109 | 0.005 | 0.032 | | 0.417 | 0.481 | 0.476 | 0.395 | 0.239 | 0.325 | | 0.947 | 0.953 | 0.867 | 0.950 | 0.968 | 0.950 | 10, 15 | | −0.035 | −0.297 | −0.239 | −0.313 | 0.019 | −0.202 | | 0.005 | 0.091 | 0.217 | 0.108 | 0.002 | 0.043 | | 0.390 | 0.433 | 0.426 | 0.390 | 0.235 | 0.323 | | 0.940 | 0.952 | 0.884 | 0.951 | 0.964 | 0.951 | 15, 10 | | 0.033 | −0.237 | 0.118 | −0.300 | 0.076 | −0.159 | | 0.003 | 0.059 | 0.014 | 0.101 | 0.007 | 0.026 | | 0.327 | 0.430 | 0.426 | 0.391 | 0.234 | 0.316 | | 0.959 | 0.951 | 0.898 | 0.953 | 0.975 | 0.950 | 20, 20 | | −0.001 | −0.307 | 0.118 | −0.297 | 0.054 | −0.196 | | 0.002 | 0.096 | 0.014 | 0.098 | 0.004 | 0.039 | | 0.321 | 0.417 | 0.421 | 0.311 | 0.225 | 0.315 | | 0.958 | 0.954 | 0.821 | 0.950 | 0.974 | 0.951 |
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