Translate a vector of coefficients from a Renewal-POT model with Pareto excesses into a vector of GEV parameters

Translate a vector of coefficients from a Renewal-POT model with Pareto excesses into a vector of GEV parameters.

Usage

Ren2gev(object,
        threshold = NULL,
        w = 1,
        distname.y = c("gpd", "GPD", "lomax", "maxlo"),
        jacobian = (length(w) == 1L),
        vcovRen = NULL)

Arguments

object

A named vector of parameters or an object of class "Renouv". In the first case, the names of the vector element must conform to the distribution given in distname.y.

threshold

The threshold associated with the renewal-POT model. This must be provided and be a non NA finite numeric value. It is the location parameter of the GPD.

w

The duration of the blocks.

distname.y

The distribution of the excesses in the renewal-POT model. This is normally a "gpd" but can be a "lomax" or a "maxlo" distribution provided that the GEV parameters given in object specify a positive or a negative shape respectively.

jacobian

Logical. If TRUE, the jacobian matrix of the transformation is computed. This is only possible at the time when w has length 1.

vcovRen

A covariance matrix for the "Ren" vector of parameters. If object has class "Renouv", then the covariance matrix embedded in the object is used.

Details

Given Renewal-POT parameters, it is possible to compute the distribution of block maxima. When the distribution is in the Pareto family, the marginal distribution of maxima is GEV. The location and the scale GEV parameters depend on the block duration \(w\), while the GEV shape parameter is identical to that of the GPD input distribution.

Value

When w has length 1, a named vector of GEV parameters as the one estimated by fgev. This vector has an elements named "loc", "scale" and "shape".

When w has length > 1, a matrix with length(w)

rows, each representing a vector of GEV parameters as before.

The returned object has attributes named "threshold". and

"distname.y" to recall how it was built.

Author

Yves Deville

Examples

fit1 <- Renouv(Garonne, distname.y = "maxlo")

Ren2gev(fit1)
#>          loc        scale        shape 
#> 3583.3875802 1167.9168446   -0.1630533 
#> attr(,"jacobian")
#>          lambda     scale         shape
#> loc   492.32939 0.1313805 -164.50127607
#> scale -80.27593 0.1416313 -163.61021404
#> shape   0.00000 0.0000000    0.02658638
#> attr(,"vcov")
#>                loc       scale        shape
#> loc   15392.775904 4185.306693 -4.699125652
#> scale  4185.306693 5573.120054 -2.901348310
#> shape    -4.699126   -2.901348  0.003824851
#> attr(,"threshold")
#> [1] 2500
fit2 <- Renouv(Garonne, distname.y = "gpd")

Ren2gev(fit2)
#>          loc        scale        shape 
#> 3582.6802262 1167.3071559   -0.1626228 
#> attr(,"jacobian")
#>          lambda     scale    shape
#> loc   492.04884 0.8059401  456.705
#> scale -80.01834 0.8689358 1008.410
#> shape   0.00000 0.0000000    1.000
#> attr(,"vcov")
#>                loc      scale        shape
#> loc   15401.445089 4202.36991 -4.713490789
#> scale  4202.369910 5578.82193 -2.911330135
#> shape    -4.713491   -2.91133  0.003837403
#> attr(,"threshold")
#> [1] 2500