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Generalized extreme value distribution (return level parametrization)

Source: R/univdist.R
gevr.Rd

Likelihood, score function and information matrix, approximate ancillary statistics and sample space derivative for the generalized extreme value distribution parametrized in terms of the return level \(z\), scale and shape.

Arguments

par

vector of retlev, scale and shape

dat

sample vector

p

tail probability, corresponding to \((1-p)\)th quantile for \(z\)

method

string indicating whether to use the expected ('exp') or the observed ('obs' - the default) information matrix.

nobs

number of observations

V

vector calculated by gevr.Vfun

Usage

gevr.ll(par, dat, p)
gevr.ll.optim(par, dat, p)
gevr.score(par, dat, p)
gevr.infomat(par, dat, p, method = c('obs', 'exp'), nobs = length(dat))
gevr.Vfun(par, dat, p)
gevr.phi(par, dat, p, V)
gevr.dphi(par, dat, p, V)

Functions

  • gevr.ll: log likelihood

  • gevr.ll.optim: negative log likelihood parametrized in terms of return levels, log(scale) and shape in order to perform unconstrained optimization

  • gevr.score: score vector

  • gevr.infomat: observed information matrix

  • gevr.Vfun: vector implementing conditioning on approximate ancillary statistics for the TEM

  • gevr.phi: canonical parameter in the local exponential family approximation

  • gevr.dphi: derivative matrix of the canonical parameter in the local exponential family approximation

Author

Leo Belzile