Renext (version 3.1-4)

RenouvNoEst: Define a 'renouvellement' model without estimation

Description

Build a 'renouvellement' model using parameters given by the user.

Usage

RenouvNoEst(threshold,
            estimate = NULL,
            distname.y = "exponential",
            fixed.par.y = NULL,
            trans.y = NULL,
            pct.conf = c(95, 70),
            rl.prob = NULL,
            prob.max = 1 - 1e-04,
            pred.period = NULL,
            cov = NULL,
            nb.OT = NULL,
            infer.method = NULL)

Value

An object of class "Renouv" representing a 'renouvellement' model similar to those built with Renouv. This is mainly a list. Note however that some list elements found in Renouv

objects built by Renouv can not be found here. For instance, the returned objects embeds no goodness-of-fit results since the object is created without making use of any data.

Arguments

threshold

The threshold.

estimate

Numeric named vector containing the estimates for the parameters. It must be compatible with the distribution chosen, and must contain in first position an element named "lambda" representing an estimated event rate in events by year.

distname.y

Character giving the name of the distribution.

fixed.par.y

Numeric named vector containing values for vectors which are considered as fixed (and not estimated).

trans.y

Transformation as in Renouv. Used only when distname.y is equal to "exponential".

pct.conf

Vector of percents for confidence limits.

rl.prob

Probability used in the return level computations. These values are used for instance in return level plots produced with the plot.Renouv method. When NULL a default vector is used.

prob.max

Maximal probability for which computations are done.

pred.period

Vector of periods for which predicted return levels will be computed.

cov

Covariance matrix for the provided estimated parameters. Must have rownames and colnames in accordance with those of estimate. This covariance matrix is used to build confidence limits on parameters and on return levels using the delta method.

nb.OT

Number of data over the threshold used for estimation. This will be used only when distname.y is equal to "exponential".

infer.method

Inference method. Will normally be the delta method.

Author

Yves Deville

Details

This function is used for plotting or comparing models with known parameter estimates but with no data available.

The parameters estimates should be accompanied with a covariance matrix assuming an approximately normal joint distribution of these. This matrix is usually obtained by computing the numerical derivatives of the log-likelihood at the second order at the estimates. This covariance is used to compute approximate confidence limits for the return levels of the unknown true distribution that was estimated.

See Also

Renouv to estimate such models.

Examples

##======================================================================
## Example from S. Coles' book, page 86 'rainfall data'.
## Note that the first parameter is here the rate 'lambda', and no the
## probability of exceedance as in Coles' book.
##======================================================================
estimate <- c(lambda = 152 / 48, scale = 7.44, shape = 0.184)          
cov <- matrix(c(4.9e-7 * (17531 / 48)^2,  0.0000,  0.0000,
                0.0000,  0.9180, -0.0655,
                0.0000, -0.0655,  0.0102),
              nrow = 3)
colnames(cov) <- rownames(cov) <- names(estimate)
renNE <- RenouvNoEst(threshold = 30, distname.y = "gpd",
                     pct.conf = c(95, 70),
                     estimate = estimate,
                     nb.OT = 152, cov = cov)
summary(renNE)
plot(renNE, main = "Daily rainfall data SW England", ylim = c(0, 400))