Generalized extreme value distribution (quantile/mean of N-block maxima parametrization)

Likelihood, score function and information matrix, approximate ancillary statistics and sample space derivative for the generalized extreme value distribution parametrized in terms of the quantiles/mean of N-block maxima parametrization \(z\), scale and shape.

Arguments

par

vector of loc, quantile/mean of N-block maximum and shape

dat

sample vector

V

vector calculated by gevN.Vfun

q

probability, corresponding to \(q\)th quantile of the N-block maximum

qty

string indicating whether to calculate the q quantile or the mean

Usage

gevN.ll(par, dat, N, q, qty = c('mean', 'quantile'))
gevN.ll.optim(par, dat, N, q = 0.5, qty = c('mean', 'quantile'))
gevN.score(par, dat, N, q = 0.5, qty = c('mean', 'quantile'))
gevN.infomat(par, dat, qty = c('mean', 'quantile'), method = c('obs', 'exp'), N, q = 0.5, nobs = length(dat))
gevN.Vfun(par, dat, N, q = 0.5, qty = c('mean', 'quantile'))
gevN.phi(par, dat, N, q = 0.5, qty = c('mean', 'quantile'), V)
gevN.dphi(par, dat, N, q = 0.5, qty = c('mean', 'quantile'), V)

Functions

• gevN.ll: log likelihood

• gevN.score: score vector

• gevN.infomat: expected and observed information matrix

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

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

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

Author

Leo Belzile