Fit an EGP model to data over a range of candidate thresholds thresh and perform likelihood-based tests of equality for \(\kappa=c\), where \(c=1\) for all regular models and $\(c=0\) for the 'gj-tnorm' and 'logist' models, for which the generalized Pareto special case corresponds to a value of \(\kappa\) occuring on the boundary of the parameter space.
thselect.egp(
xdat,
thresh,
model = c("pt-beta", "pt-gamma", "pt-power", "gj-tnorm", "gj-beta", "exptilt",
"logist"),
type = c("wald", "lrt"),
level = 0.95,
transform = FALSE,
plot = FALSE,
...
)an invisible list of class mev_thselect_egp with elements
thresh: vector of threshold candidates
thresh0: selected threshold among candidates
coef: vector of parameter estimates for \(\kappa\)
stat: squared version of the test statistic
pval: p-value obtained from the \(\chi^2_1\) approximation
level: level of the confidence intervals
model: string giving the EGP model family
type: type of confidence interval
vector of observations, greater than the threshold
threshold value
a string indicating which extended family to fit
choice of test statistic, either wald for Wald-based intervals, or lrt for profile likelihood ratio test.
[double] confidence interval level, default to 0.95.
logical; if TRUE and type="wald", intervals for kappa are computed on the log-scale and back-transformed.
[logical] if TRUE, return a plot of p-values against threshold
additional arguments, passed to plotting routine
The threshold selection procedure returns chi-square statistics (stat) for Wald or profile likelihood ratio tests, along with p-values (pval) obtained from large sample distribution. The threshold returned is the lowest for which all further higher thresholds fail to reject the null hypothesis of \(\kappa=c\), or equivalently of generalized Pareto tail.
ths <- thselect.egp(
xdat = rexp(1000),
thresh = qexp(c(0.8,0.9,0.95)),
model = "pt-power")
print(ths)
plot(ths)
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