gpdN {mev}

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

Description

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(s)

Leo Belzile