Translate a vector of coefficients from a Renewal-POT model with exponential excesses to a vector of Gumbel parameters

Translate a vector of coefficients from a Renewal-POT model with exponential excesses to a vector of Gumbel parameters.

Usage

Ren2gumbel(object,
           threshold = NULL,
           w = 1,
           distname.y = c("exponential", "exp"),
           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 exponential distribution so the vector must be of length 2 with names "lambda" and "rate".

threshold

A threshold associated with the parameters. If object is an object with class "Renouv", its threshold slot will be used.

w

A block duration or a vector of block durations.

distname.y

The name of the distribution for the excesses. Can be either "exponential" or "exp". The choice has no impact on the computations, but this name will be attached to the result as an attribute and may affect later use.

jacobian

Logical. If TRUE the jacobian matrix of the transformation will be computed and attached to the result as an attribute.

vcovRen

A covariance matrix for the Renouv parameters.

Value

A vector of GEV parameters if w has length 1, and a matrix if w has length > 1. The returned objects has attributes.

Author

Yves Deville

Examples

## Fit a Renouv model with exponential excesses (default)
fit <- Renouv(Garonne)

## Convert to gumbel (usable for one-year block maxima)
parGumbel <- Ren2gumbel(fit)
## Retrieve the 'Renouv' model by giving the right threshold
parRen <- gumbel2Ren(parGumbel,
                     threshold = 2500,
                     vcovGumbel = attr(parGumbel, "vcov"),
                     plot = TRUE)

#>            loc    scale
#> loc   8719.318 2564.989
#> scale 2564.989 4116.247
#>                   loc         scale
#> lambda    0.002173328 -1.849022e-03
#> threshold 1.000000000  0.000000e+00
#> rate      0.000000000 -8.615349e-07
#>              lambda         rate
#> lambda 3.464240e-02 1.754489e-06
#> rate   1.754489e-06 3.055253e-09
## Build a compatible model under the assumption of one event by
## year
parRen2 <- gumbel2Ren(parGumbel,
                      lambda = 1.00,
                      vcovGumbel = attr(parGumbel, "vcov"),
                      plot = TRUE)

#>            loc    scale
#> loc   8719.318 2564.989
#> scale 2564.989 4116.247
#>           loc         scale
#> lambda      0  0.000000e+00
#> threshold   1  0.000000e+00
#> rate        0 -8.615349e-07
#>        lambda         rate
#> lambda      0 0.000000e+00
#> rate        0 3.055253e-09
parRenNames <- c("lambda", "rate")
## Build a 'Renouv' object without estimation
myVcov <- attr(parRen, "vcov")[parRenNames, parRenNames]
fitNew <- RenouvNoEst(threshold = attr(parRen, "threshold"),
                      estimate = parRen,
                      distname.y = "exp",
                      cov = myVcov)
#> Warning: warning: distribution not in target list. Still EXPERIMENTAL
## Compare return levels
cbind(roundPred(fit$pred)[ , -2], roundPred(fitNew$pred)[ , -2])
#>    period L.95  U.95  L.70  U.70 period L.95  U.95  L.70  U.70
#> 30     10 5494  6300  5684  6110     10 5501  6293  5688  6107
#> 33     20 6160  7128  6388  6900     20 6161  7127  6389  6900
#> 36     50 7038  8224  7318  7945     50 7033  8230  7315  7948
#> 38    100 7701  9055  8020  8736    100 7693  9063  8016  8740
#> 41    200 8363  9887  8722  9528    200 8352  9897  8716  9533
#> 43    300 8750 10373  9132  9991    300 8738 10385  9126  9997
#> 44    400 9024 10719  9424 10320    400 9012 10731  9417 10326
#> 46    500 9237 10987  9649 10575    500 9225 11000  9643 10581
#> 47    600 9411 11206  9834 10783    600 9398 11219  9827 10790
#> 48    700 9558 11391  9990 10959    700 9545 11404  9983 10966
#> 49    800 9686 11551 10125 11112    800 9672 11565 10118 11119
#> 51    900 9798 11693 10244 11246    900 9784 11707 10237 11254
#> 52   1000 9898 11819 10351 11367   1000 9884 11833 10343 11374
## idem for the putative 'Renouv' with rate 1
myVcov2 <- attr(parRen2, "vcov")[parRenNames, parRenNames]
fitNew2 <- RenouvNoEst(threshold = attr(parRen2, "threshold"),
                       estimate = parRen2,
                       distname.y = "exp",
                       cov = myVcov2)
#> Warning: warning: distribution not in target list. Still EXPERIMENTAL
cbind(roundPred(fit$pred)[ , -2], roundPred(fitNew2$pred)[ , -2])
#>    period L.95  U.95  L.70  U.70 period L.95  U.95  L.70  U.70
#> 30     10 5494  6300  5684  6110     10 5608  6187  5744  6050
#> 33     20 6160  7128  6388  6900     20 6268  7020  6445  6843
#> 36     50 7038  8224  7318  7945     50 7140  8123  7371  7891
#> 38    100 7701  9055  8020  8736    100 7800  8957  8072  8684
#> 41    200 8363  9887  8722  9528    200 8459  9790  8773  9477
#> 43    300 8750 10373  9132  9991    300 8845 10278  9183  9941
#> 44    400 9024 10719  9424 10320    400 9119 10624  9474 10270
#> 46    500 9237 10987  9649 10575    500 9331 10893  9699 10525
#> 47    600 9411 11206  9834 10783    600 9505 11112  9884 10733
#> 48    700 9558 11391  9990 10959    700 9652 11297 10039 10910
#> 49    800 9686 11551 10125 11112    800 9779 11458 10174 11062
#> 51    900 9798 11693 10244 11246    900 9891 11600 10293 11197
#> 52   1000 9898 11819 10351 11367   1000 9991 11726 10400 11318