# identifiability: Identifiability of two-parameter copula families In CopulaInference: Estimation and Goodness-of-Fit of Copula-Based Models with Arbitrary Distributions

 identifiability R Documentation

## Identifiability of two-parameter copula families

### Description

Determines if a copula family is identifiable with respect to the empirical margins. One-parameter copula families ("gaussian","gumbel","clayton","frank","plackett","joe") are identifiable whatever the margins. The rank of the gradient of the copula on the range of the margins is evaluated at 10000 parameter points within the lower and upper bounds of the copula family.

### Usage

``````identifiability(data = NULL, family, rotation = 0, Fx = NULL, Fy = NULL)
``````

### 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", "plackettâ€ť, "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). `Fy` Marginal cdf function applied to Y (default is NULL).

### Value

 `out` True or False

### References

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

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

### Examples

``````set.seed(1)
data = matrix(rpois(20,1),ncol=2)
out = identifiability(data,"gumbel")

``````

CopulaInference documentation built on April 21, 2023, 9:07 a.m.