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The parameters of the P3 marginal distributions were estimated by L-moment method and are listed in Table 1. A chi-square goodness-of-fit and the Kolmogorov–Smirnov (K–S) test are used to test the assumption. The results in Table 2 show that the hypothesis could not be rejected at the 5% significance level because , and the P3 distributions can also pass the K–S test because Dn < Dn,0.95. The marginal distribution frequency curves of flood peak and 7-day flood volumes are shown in Figure 4, in which the line represents the theoretical distribution and the crosses represent empirical probabilities. Figure 4 indicates that these theoretical distributions can fit the observed data reasonably well.
Table 1

Sample statistic values and estimated parameters of P3 distribution in Geheyan reservoir

VariablesSample statistic values
P3 parameters
MeanL-CvL-CsαΒδ
Qp (m3/s) 7,820 0.4 1.2 2.78 0.0005 2606.7 
W7 (108 m317 0.5 1.5 1.78 0.1569 5.7 
VariablesSample statistic values
P3 parameters
MeanL-CvL-CsαΒδ
Qp (m3/s) 7,820 0.4 1.2 2.78 0.0005 2606.7 
W7 (108 m317 0.5 1.5 1.78 0.1569 5.7 
Table 2

Hypothesis test results of P3 marginal distribution for flood peak and volume

VariablesChi-square test
K–S test
χ20.05Chi-square statistics, χ2Dn,0.95Dn
Qp (m3/s) 7.815 5.313 0.185 0.096 
W7 (108 m39.488 3.396 0.185 0.078 
VariablesChi-square test
K–S test
χ20.05Chi-square statistics, χ2Dn,0.95Dn
Qp (m3/s) 7.815 5.313 0.185 0.096 
W7 (108 m39.488 3.396 0.185 0.078 
Figure 4

Probability curves of flood peak and 7-day flood volume.

Figure 4

Probability curves of flood peak and 7-day flood volume.

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