Likelihood, score function and information matrix, bias, approximate ancillary statistics and sample space derivative for the generalized Pareto distribution
vector of scale and shape
sample vector
numerical tolerance for the exponential model
string indicating whether to use the expected ('exp') or the observed ('obs' - the default) information matrix.
vector calculated by gpd.Vfun
sample size
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)
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
Leo Belzile
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.