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Generalized Pareto distribution

Source: R/univdist.R
gpd.Rd

Likelihood, score function and information matrix, bias, approximate ancillary statistics and sample space derivative for the generalized Pareto distribution

Arguments

par

vector of scale and shape

dat

sample vector

tol

numerical tolerance for the exponential model

method

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

V

vector calculated by gpd.Vfun

n

sample size

Usage

gpd.ll(par, dat, tol=1e-5)
gpd.ll.optim(par, dat, tol=1e-5)
gpd.score(par, dat)
gpd.infomat(par, dat, method = c('obs','exp'))
gpd.bias(par, n)
gpd.Fscore(par, dat, method = c('obs','exp'))
gpd.Vfun(par, dat)
gpd.phi(par, dat, V)
gpd.dphi(par, dat, V)

Functions

  • gpd.ll: log likelihood

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

  • gpd.score: score vector

  • gpd.infomat: observed or expected information matrix

  • gpd.bias: Cox-Snell first order bias

  • gpd.Fscore: Firth's modified score equation

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

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

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

References

Firth, D. (1993). Bias reduction of maximum likelihood estimates, Biometrika, 80(1), 27–38.

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

Cox, D. R. and E. J. Snell (1968). A general definition of residuals, Journal of the Royal Statistical Society: Series B (Methodological), 30, 248–275.

Cordeiro, G. M. and R. Klein (1994). Bias correction in ARMA models, Statistics and Probability Letters, 19(3), 169–176.

Giles, D. E., Feng, H. and R. T. Godwin (2016). Bias-corrected maximum likelihood estimation of the parameters of the generalized Pareto distribution, Communications in Statistics - Theory and Methods, 45(8), 2465–2483.

Author

Leo Belzile