gpdr {mev}

Generalized Pareto distribution (return level parametrization)

Description

Likelihood, score function and information matrix, approximate ancillary statistics and sample space derivative for the generalized Pareto distribution parametrized in terms of return levels.

Arguments

par

vector of length 2 containing y_m and \xi, respectively the m-year return level and the shape parameter.

dat

sample vector

m

number of observations of interest for return levels. See Details

tol

numerical tolerance for the exponential model

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 gpdr.Vfun

Details

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

The interpretation for m is as follows: if there are on average m_y observations per year above the threshold, then m=Tm_y corresponds to T-year return level.

Usage

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

Functions

• gpdr.ll: log likelihood

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

• gpdr.score: score vector

• gpdr.infomat: observed information matrix for GPD parametrized in terms of rate of m-year return level and shape

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

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

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

Author(s)

Leo Belzile