Frequency Band (Hz) | Mahalanobis Distance | Misclassification Probability (%) | F-Distribution (F(x) = 95%) | χ2 Approximation from Data vs. χ2 from Table (for F(x) = 95%) |
---|---|---|---|---|
1–4* | 4.64 | 14.07 | 6.01 > 2.90 | 6.80 < 18.31/2 |
2–5† | 6.55 | 10.04 | 8.48 > 2.90 | 2.94 < 18.31/2 |
3–6‡ | 16.31 | 2.17 | 21.13 > 2.90 | 14.95 > 18.31/2 |
4–7 | 12.61 | 3.79 | 16.33 > 2.90 | 3.98 < 18.31/2 |
5–8 | 14.69 | 2.76 | 19.03 > 2.90 | 3.36 < 18.31/2 |
6–9 | 25.60§ | 0.57§ | 33.17 > 2.90 | 2.66 < 18.31/2 |
7–10 | 24.28 | 0.69 | 31.46 > 2.90 | 6.61 < 18.31/2 |
8–11 | 23.75 | 0.74 | 30.76 > 2.90 | 3.64 < 18.31/2 |
9–12 | 20.44 | 1.19 | 26.47 > 2.90 | 0.62 < 18.31/2 |
10–13 | 11.80 | 4.29 | 15.29 > 2.90 | 9.20 ~ 18.31/2 |
11–14 | 11.80 | 4.29 | 15.28 > 2.90 | 5.22 < 18.31/2 |
12–15 | 13.07 | 3.53 | 16.93 > 2.90 | 5.47 < 18.31/2 |
* For frequencies 1–4 Hz, one earthquake and one explosion were misclassified.
† For frequencies 2–5 Hz, two earthquakes were misclassified (but no explosions).
‡ For frequencies 3–6 Hz, one explosion was misclassified (but no earthquakes). The frequency band 3–6 Hz is not useful for linear discriminant function (LDF) analysis, because it does not satisfy the null hypothesis that the dispersion matrices are the same.
§ Frequencies and values of Δ2 and misclassification used for analysis in the main article.
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