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Generalized Pareto distribution (mean of maximum of N exceedances parametrization)

Source: R/univdist.R
gpdN.Rd

Likelihood, score function and information matrix, approximate ancillary statistics and sample space derivative for the generalized Pareto distribution parametrized in terms of average maximum of N exceedances.

The parameter N corresponds to the number of threshold exceedances of interest over which the maxima is taken. \(z\) is the corresponding expected value of this block maxima. Note that the actual parametrization is in terms of excess expected mean, meaning expected mean minus threshold.

Arguments

par

vector of length 2 containing \(z\) and \(\xi\), respectively the mean excess of the maxima of N exceedances above the threshold and the shape parameter.

dat

sample vector

N

block size for threshold exceedances.

tol

numerical tolerance for the exponential model

V

vector calculated by gpdN.Vfun

Details

The observed information matrix was calculated from the Hessian using symbolic calculus in Sage.

Usage

gpdN.ll(par, dat, N, tol=1e-5)
gpdN.score(par, dat, N)
gpdN.infomat(par, dat, N, method = c('obs', 'exp'), nobs = length(dat))
gpdN.Vfun(par, dat, N)
gpdN.phi(par, dat, N, V)
gpdN.dphi(par, dat, N, V)

Functions

  • gpdN.ll: log likelihood

  • gpdN.score: score vector

  • gpdN.infomat: observed information matrix for GP parametrized in terms of mean of the maximum of N exceedances and shape

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

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

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

Author

Leo Belzile