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In these hypothetical test cases, for simplicity, the analyses were undertaken via selecting two points from each data set. As explained in the previous section, the use of more data points inside the integration window would yield more accurate area approximations. The AMP procedure was followed for all available distinct data sets to obtain the estimation results as depicted in Figure 5 and tabulated in Table 2. The integration intervals employed in this numerical experiment represent different phases of the test data of interest as given in Table 2.
Table 2

AMP performance for noisy data set

 Random noise 1%
Random noise 2%
Integration window ΔRMSER2Max. absolute errorMin. absolute errorRMSER2Max. absolute errorMin. absolute error
0.038236 0.99998 0.10198 0.025218 0.046597 0.99993 0.1045 0.04391 
1.9 0.036664 0.99998 0.095022 0.01829 0.047807 0.99991 0.11212 0.051904 
1.8 0.035968 0.99997 0.086503 0.020317 0.043687 0.99994 0.10625 0.053386 
1.7 0.032834 0.99997 0.071714 0.035084 0.038576 0.99994 0.087383 0.039419 
1.6 0.031393 0.99997 0.067473 0.028837 0.043244 0.9999 0.092132 0.064931 
1.5 0.035054 0.99996 0.07251 0.04861 0.046852 0.99988 0.11187 0.08252 
1.4 0.032485 0.99996 0.080356 0.052118 0.049636 0.99987 0.13125 0.066414 
1.3 0.030346 0.99997 0.074189 0.036482 0.060511 0.99974 0.14698 0.092399 
1.2 0.025799 0.99997 0.061173 0.03712 0.057813 0.99977 0.16323 0.091952 
1.1 0.035 0.99993 0.078924 0.069239 0.063327 0.99975 0.19781 0.089668 
0.033992 0.99993 0.089567 0.072161 0.073062 0.99965 0.25116 0.10891 
0.9 0.035418 0.99992 0.079144 0.07767 0.080256 0.99956 0.3049 0.11918 
0.8 0.041939 0.99987 0.12012 0.072232 0.10196 0.99936 0.32052 0.15949 
0.7 0.04468 0.99985 0.17545 0.073699 0.094512 0.99931 0.31285 0.19458 
0.6 0.049217 0.99981 0.15348 0.11415 0.10597 0.9991 0.3755 0.17737 
0.5 0.056996 0.99974 0.14103 0.13023 0.1462 0.99843 0.67589 0.25183 
 Random noise 1%
Random noise 2%
Integration window ΔRMSER2Max. absolute errorMin. absolute errorRMSER2Max. absolute errorMin. absolute error
0.038236 0.99998 0.10198 0.025218 0.046597 0.99993 0.1045 0.04391 
1.9 0.036664 0.99998 0.095022 0.01829 0.047807 0.99991 0.11212 0.051904 
1.8 0.035968 0.99997 0.086503 0.020317 0.043687 0.99994 0.10625 0.053386 
1.7 0.032834 0.99997 0.071714 0.035084 0.038576 0.99994 0.087383 0.039419 
1.6 0.031393 0.99997 0.067473 0.028837 0.043244 0.9999 0.092132 0.064931 
1.5 0.035054 0.99996 0.07251 0.04861 0.046852 0.99988 0.11187 0.08252 
1.4 0.032485 0.99996 0.080356 0.052118 0.049636 0.99987 0.13125 0.066414 
1.3 0.030346 0.99997 0.074189 0.036482 0.060511 0.99974 0.14698 0.092399 
1.2 0.025799 0.99997 0.061173 0.03712 0.057813 0.99977 0.16323 0.091952 
1.1 0.035 0.99993 0.078924 0.069239 0.063327 0.99975 0.19781 0.089668 
0.033992 0.99993 0.089567 0.072161 0.073062 0.99965 0.25116 0.10891 
0.9 0.035418 0.99992 0.079144 0.07767 0.080256 0.99956 0.3049 0.11918 
0.8 0.041939 0.99987 0.12012 0.072232 0.10196 0.99936 0.32052 0.15949 
0.7 0.04468 0.99985 0.17545 0.073699 0.094512 0.99931 0.31285 0.19458 
0.6 0.049217 0.99981 0.15348 0.11415 0.10597 0.9991 0.3755 0.17737 
0.5 0.056996 0.99974 0.14103 0.13023 0.1462 0.99843 0.67589 0.25183 
Figure 5

The estimation performance of AMP.

Figure 5

The estimation performance of AMP.

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