GofBiCop {CopulaInference} | R Documentation |

## Goodness-of-fit for bivariate copula-based models with arbitrary distributions

### Description

Goodness-of-fit tests for copula-based models for data with arbitrary distributions. The tests statistics are the Cramer-von Mises statistic (Sn), the difference between the empirical Kendall's tau and the theoretical one, and the difference between the empirical Spearman's rho and the theoretical one.

### Usage

```
GofBiCop(
data = NULL,
family,
rotation = 0,
Fx = NULL,
Fxm = NULL,
Fy = NULL,
Fym = NULL,
B = 100,
n_cores = 1
)
```

### Arguments

`data` |
Matrix or data frame with 2 columns (X,Y). Can be pseudo-observations. If NULL, Fx and Fy must be provided. |

`family` |
Copula family: "gaussian", "t", "clayton", "frank", "gumbel", "joe", "plackett”, "bb1", "bb6", "bb7","bb8","ncs-gaussian", "ncs-clayton", "ncs-gumbel", "ncs-frank", "ncs-joe","ncs-plackett". |

`rotation` |
Rotation: 0 (default value), 90, 180, or 270. |

`Fx` |
marginal cdf function applied to X (default is NULL). |

`Fxm` |
left limit of marginal cdf function applied to X default is NULL). |

`Fy` |
marginal cdf function applied to Y (default is NULL). |

`Fym` |
left limit of marginal cdf function applied to Y (default is NULL). |

`B` |
Number of bootstrap samples (default 100) |

`n_cores` |
Number of cores to be used for parallel computing (default is 1). |

### Value

`pvalueSn` |
Pvalue of Sn in percent |

`pvalueTn` |
Pvalue of Tn in percent |

`pvalueRn` |
Pvalue of Rn in percent |

`Sn` |
Value of Cramer-von Mises statistic Sn |

`Tn` |
Value of Kendall's statistic Tn |

`Rn` |
Value of Spearman's statistic Rn |

`cpar` |
Copula parameters |

`family` |
Copula family |

`rotation` |
Rotation value |

`tauth` |
Kendall's tau (from the multilinear theoretical copula) |

`tauemp` |
Empirical Kendall's tau (from the multilinear empirical copula) |

`rhoth` |
Spearman's rho (from the multilinear theoretical copula) |

`rhoemp` |
Empirical Spearman's rho (from the multilinear empirical copula) |

`parB` |
Bootstrapped parameters |

`loglik` |
Log-likelihood |

`aic` |
AIC value |

`bic` |
BIC value |

### References

Nasri & Remillard (2023). Identifiability and inference for copula-based semiparametric models for random vectors with arbitrary marginal distributions. arXiv 2301.13408.

Nasri & Remillard (2023). Goodness-of-fit and bootstrapping for copula-based random vectors with arbitrary marginal distributions.

Nasri (2020). On non-central squared copulas. Statistics and Probability Letters.

### Examples

```
data = rvinecopulib::rbicop(10,"gumbel",rotation=0,2)
out=GofBiCop(data,family="gumbel",B=10)
```

*CopulaInference*version 0.5.0 Index]