pp {mev}

Poisson process of extremes.

Description

Likelihood, score function and information matrix for the Poisson process likelihood.

Arguments

par

vector of loc, scale and shape

dat

sample vector

u

threshold

method

string indicating whether to use the expected ('exp') or the observed ('obs' - the default) information matrix.

np

number of periods of observations. This is a post hoc adjustment for the intensity so that the parameters of the model coincide with those of a generalized extreme value distribution with block size length(dat)/np.

nobs

number of observations for the expected information matrix. Default to length(dat) if dat is provided.

Usage

pp.ll(par, dat)
pp.ll(par, dat, u, np)
pp.score(par, dat)
pp.infomat(par, dat, method = c('obs', 'exp'))

Functions

• pp.ll: log likelihood

• pp.score: score vector

• pp.infomat: observed or expected information matrix

Author(s)

Leo Belzile

References

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

Wadsworth, J.L. (2016). Exploiting Structure of Maximum Likelihood Estimators for Extreme Value Threshold Selection, Technometrics, 58(1), 116-126, http://dx.doi.org/10.1080/00401706.2014.998345.

Sharkey, P. and J.A. Tawn (2017). A Poisson process reparameterisation for Bayesian inference for extremes, Extremes, 20(2), 239-263, http://dx.doi.org/10.1007/s10687-016-0280-2.