Tangent exponential model approximation for the GEV distribution

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

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

plot

logical indiating whether plot.fr should be called upon exit

Value

an 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

  • param: parameter

Author(s)

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

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