# profconf: Profiled Confidence interval for the GP Distribution In POT: Generalized Pareto Distribution and Peaks Over Threshold

 Profiled Confidence Intervals R Documentation

## Profiled Confidence interval for the GP Distribution

### Description

Compute profiled confidence intervals on parameter and return level for the GP distribution. This is achieved through the profile likelihood procedure.

### Usage

```gpd.pfshape(object, range, xlab, ylab, conf = 0.95, nrang = 100,
vert.lines = TRUE, ...)
gpd.pfscale(object, range, xlab, ylab, conf = 0.95, nrang = 100,
vert.lines = TRUE, ...)
gpd.pfrl(object, prob, range, thresh, xlab, ylab, conf = 0.95, nrang =
100, vert.lines = TRUE, ...)
```

### Arguments

 `object` `R` object given by function `fitgpd`. `prob` The probability of non exceedance. `range` Vector of dimension two. It gives the lower and upper bound on which the profile likelihood is performed. `thresh` Optional. The threshold. Only needed with non constant threshold. `xlab, ylab` Optional Strings. Allows to label the x-axis and y-axis. If missing, default value are considered. `conf` Numeric. The confidence level. `nrang` Numeric. It specifies the number of profile likelihood computed on the whole range `range`. `vert.lines` Logical. If `TRUE` (the default), vertical lines are plotted. `...` Optional parameters to be passed to the `plot` function.

### Value

Returns a vector of the lower and upper bound for the profile confidence interval. Moreover, a graphic of the profile likelihood function is displayed.

Mathieu Ribatet

### References

Coles, S. (2001). An Introduction to Statistical Modelling of Extreme Values. Springer Series in Statistics. London.

`gpd.fiscale`, `gpd.fishape`, `gpd.firl` and `confint`

### Examples

```data(ardieres)
events <- clust(ardieres, u = 4, tim.cond = 8 / 365,
clust.max = TRUE)
MLE <- fitgpd(events[, "obs"], 4, 'mle')
gpd.pfshape(MLE, c(0, 0.8))
rp2prob(10, 2)
gpd.pfrl(MLE, 0.95, c(12, 25))
```

POT documentation built on April 14, 2022, 5:07 p.m.