EllCopLikelihood {ElliptCopulas} | R Documentation |

## Computation of the likelihood of an elliptical copula

### Description

Computes the likelihood

```
\frac{g(Q_g(U) \Sigma^{-1} Q_g(U))}{f_g(Q_g(U_1)) \cdots f_g(Q_g(U_d))}
```

for a vector `(U_1, \dots, U_d)`

on the unit cube
and for a `d`

-dimensional generator `g`

whose univariate density and quantile functions
are respectively `f_g`

and `Q_g`

.
This is to the likelihood of the copula associated with the elliptical distribution
having density `|det(\Sigma)|^{-1/2} g(x \Sigma^{-1} x)`

.

### Usage

```
EllCopLikelihood(grid, g_d, pointsToCompute, Sigma_m1, log = TRUE)
```

### Arguments

`grid` |
the discretization grid on which the generator is given. |

`g_d` |
the values of the |

`pointsToCompute` |
the points |

`Sigma_m1` |
the inverse correlation matrix of the elliptical distribution. |

`log` |
if |

### Value

a vector (of length 1 if `pointsToCompute`

is a vector) of likelihoods
associated with each observation.

### References

Derumigny, A., & Fermanian, J. D. (2022). Identifiability and estimation of meta-elliptical copula generators. Journal of Multivariate Analysis, article 104962. doi:10.1016/j.jmva.2022.104962.

### See Also

`EllCopEst`

for the estimation of elliptical copula,
`EllCopEst`

for the estimation of elliptical copula.

### Examples

```
grid = seq(0,50,by = 0.01)
gdnorm = DensityGenerator.normalize(grid = grid, grid_g = exp(-grid/2), d = 3)
gdnorm2 = DensityGenerator.normalize(grid = grid, grid_g = 1/(1+grid^2), d = 3)
X = EllCopSim(n = 30, d = 3, grid = grid, g_d = gdnorm)
logLik = EllCopLikelihood(grid , g_d = gdnorm , X,
Sigma_m1 = diag(3), log = TRUE)
logLik2 = EllCopLikelihood(grid , g_d = gdnorm2 , X,
Sigma_m1 = diag(3), log = TRUE)
print(c(sum(logLik), sum(logLik2)))
```

*ElliptCopulas*version 0.1.3 Index]