The function egp.fitrange provides classical parameter stability plot for (\(\kappa\), \(\sigma\), \(\xi\)). The fitted parameter values are displayed with pointwise normal 95% confidence intervals.
The plot is for the modified scale (as in the generalised Pareto model) and as such it is possible that the modified scale be negative.
egp.fitrange can also be used to fit the model to multiple thresholds.
egp.fit(xdat, thresh, model = c("egp1", "egp2", "egp3"), init)egp.fitrange(xdat, thresh, model = c("egp1", "egp2", "egp3"), plots = 1:3,
umin, umax, nint)
vector of observations, greater than the threshold
threshold value
a string indicating which extended family to fit
vector of initial values, with \(\log(\kappa)\) and \(\log(\sigma)\); can be omitted.
vector of integers specifying which parameter stability to plot (if any); passing NA results in no plots
optional minimum value considered for threshold (if thresh is not provided)
optional maximum value considered for threshold (if thresh is not provided)
optional integer number specifying the number of thresholds to test.
egp.fit outputs the list returned by optim, which contains the parameter values, the hessian and in addition the standard errors
egp.fitrange returns a plot(s) of the parameters fit over the range of provided thresholds, with pointwise normal confidence intervals; the function also returns an invisible list containing notably the matrix of point estimates (par) and standard errors (se).
egp.fit is a numerical optimization routine to fit the extended generalised Pareto models of Papastathopoulos and Tawn (2013),
using maximum likelihood estimation.
Papastathopoulos, I. and J. Tawn (2013). Extended generalised Pareto models for tail estimation, Journal of Statistical Planning and Inference 143(3), 131--143.