Official Journal of the Asia Oceania Geosciences Society (AOGS)
Table 8 Joint CDF and Tand estimated from the empirical copula and MECC
From: Copula–entropy theory for multivariate stochastic modeling in water engineering
C(u,v) | P (discharge) | ||||
|---|---|---|---|---|---|
P = 0.8 | P = 0.9 | P = 0.96 | P = 0.98 | ||
P (volume) | |||||
Empirical | P = 0.8 | 0.7500 | 0.7857 | 0.8036 | 0.8036 |
P = 0.9 | 0.8036 | 0.8750 | 0.9107 | 0.9107 | |
P = 0.96 | 0.8036 | 0.9107 | 0.9464 | 0.9643 | |
P = 0.98 | 0.8036 | 0.9107 | 0.9643 | 0.9821 | |
MECC | P = 0.8 | 0.7503 | 0.7861 | 0.7940 | 0.7953 |
P = 0.9 | 0.7861 | 0.8649 | 0.8946 | 0.9013 | |
P = 0.96 | 0.7940 | 0.8946 | 0.9429 | 0.9557 | |
P = 0.98 | 0.7953 | 0.9013 | 0.9557 | 0.9709 | |
Tand (years) | Discharge (cms) | ||||
|---|---|---|---|---|---|
73.20 | 109.90 | 170.66 | 230.59 | ||
Volume (m3) | |||||
Empirical | 3.18 × 105 | 6.6667 | 11.6667 | 22.9508 | 42.4242 |
4.60 × 105 | 9.6552 | 13.3333 | 19.7183 | 32.5581 | |
6.44 × 105 | 22.9508 | 19.7183 | 37.8378 | 41.1765 | |
7.71 × 105 | 42.4242 | 32.5581 | 41.1765 | 45.1613 | |
MECC | 3.18 × 105 | 6.6535 | 11.6146 | 29.4142 | 65.3461 |
4.60 × 105 | 11.6146 | 15.3998 | 28.9062 | 46.8990 | |
6.44 × 105 | 29.4142 | 28.9062 | 43.6433 | 63.4992 | |
7.71 × 105 | 65.3462 | 46.8990 | 63.4992 | 91.8599 | |