As introduced in the section ‘Change point detection based on Archimedean copulas’, the Gev, Logn, and Gam distributions were used to fit monthly precipitation and runoff with little difference among the three marginal distributions (Figure 4). To obtain a better marginal distribution, the RMSE and AIC for monthly runoff and precipitation were calculated and are listed in Table 2. It can be easily seen from Table 2 that the Gam and Logn distributions are the more appropriate marginal distributions because of the smaller RMSE and AIC.

Table 2

Hydrological variables . | Model of marginal distribution . | RMSE . | AIC . |
---|---|---|---|

Monthly precipitation | Gev | 0.048 | −1611.35 |

Logn | 0.061 | −1485.58 | |

Gam | 0.028 | −1906.21 | |

Monthly runoff | Gev | 0.018 | −2138.10 |

Logn | 0.012 | −2342.58 | |

Gam | 0.047 | −1625.78 |

Hydrological variables . | Model of marginal distribution . | RMSE . | AIC . |
---|---|---|---|

Monthly precipitation | Gev | 0.048 | −1611.35 |

Logn | 0.061 | −1485.58 | |

Gam | 0.028 | −1906.21 | |

Monthly runoff | Gev | 0.018 | −2138.10 |

Logn | 0.012 | −2342.58 | |

Gam | 0.047 | −1625.78 |

Figure 4

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