gev: Generalized extreme value distribution

Description

Likelihood, score function and information matrix, bias, approximate ancillary statistics and sample space derivative for the generalized extreme value distribution

Arguments

par: vector of loc, scale and shape
dat: sample vector
method: string indicating whether to use the expected ('exp') or the observed ('obs' - the default) information matrix.
V: vector calculated by gev.Vfun
n: sample size
p: vector of probabilities

Usage

gev.ll(par, dat)
gev.ll.optim(par, dat)
gev.score(par, dat)
gev.infomat(par, dat, method = c('obs','exp'))
gev.retlev(par, p)
gev.bias(par, n)
gev.Fscore(par, dat, method=c('obs','exp'))
gev.Vfun(par, dat)
gev.phi(par, dat, V)
gev.dphi(par, dat, V)

Functions

gev.ll: log likelihood
gev.ll.optim: negative log likelihood parametrized in terms of location, log(scale) and shape in order to perform unconstrained optimization
gev.score: score vector
gev.infomat: observed or expected information matrix
gev.retlev: return level, corresponding to the \((1-p)\)th quantile
gev.bias: Cox-Snell first order bias
gev.Fscore: Firth's modified score equation
gev.Vfun: vector implementing conditioning on approximate ancillary statistics for the TEM
gev.phi: canonical parameter in the local exponential family approximation
gev.dphi: derivative matrix of the canonical parameter in the local exponential family approximation

References

Firth, D. (1993). Bias reduction of maximum likelihood estimates, Biometrika, 80(1), 27--38.

Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values, Springer, 209 p.

Cox, D. R. and E. J. Snell (1968). A general definition of residuals, Journal of the Royal Statistical Society: Series B (Methodological), 30, 248--275.

Cordeiro, G. M. and R. Klein (1994). Bias correction in ARMA models, Statistics and Probability Letters, 19(3), 169--176.