# gev.tem: Tangent exponential model approximation for the GEV...

Description Usage Arguments Value Author(s) Examples

### Description

The function gev.tem provides a tangent exponential model (TEM) approximation for higher order likelihood inference for a scalar parameter for the generalized extreme value distribution. Options include location scale and shape parameters as well as value-at-risk (or return levels). The function attempts to find good values for psi that will cover the range of options, but the fail may fit and return an error.

### Usage

 1 2 gev.tem(param = c("loc", "scale", "shape", "VaR"), dat, psi = NULL, p = NULL, n.psi = 50, plot = TRUE, correction = TRUE) 

### Arguments

 param parameter over which to profile dat sample vector for the GEV distribution psi scalar or ordered vector of values for the interest parameter. If NULL (default), a grid of values centered at the MLE is selected p probability associated with the (1-p)th quantile for return levels if param="VaR". n.psi number of values of psi at which the likelihood is computed, if psi is not supplied (NULL). Odd values are more prone to give rise to numerical instabilities near the MLE. If psi is a vector of length 2 and n.psi is greater than 2, these are taken to be endpoints of the sequence. plot logical indicating whether plot.fr should be called upon exit correction logical indicating whether spline.corr should be called.

### Value

an invisible object of class fr (see tem) with elements

• normal: maximum likelihood estimate and standard error of the interest parameter psi

• par.hat: maximum likelihood estimates

• par.hat.se: standard errors of maximum likelihood estimates

• th.rest: estimated maximum profile likelihood at (psi,\hat{λ})

• r: values of likelihood root corresponding to ψ

• psi: vector of interest parameter

• q: vector of likelihood modifications

• rstar: modified likelihood root vector

• rstar.old: uncorrected modified likelihood root vector

• param: parameter

### Author(s)

Leo Belzile, from code by A. Davison from the hoa package

### Examples

 1 2 3 4 5 6 7 8 9 dat <- evd::rgev(n=40, loc=0, scale=2, shape=-0.1) gev.tem("shape",dat=dat, plot=TRUE) ## Not run: gev.tem("VaR",dat=dat, p=0.01,plot=TRUE) dat <- evd::rgev(n=40, loc=0, scale=2, shape=0.2) gev.tem("shape",dat=dat, plot=TRUE) gev.tem("VaR",dat=dat, p=0.01,plot=TRUE) ## End(Not run) 

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