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

## Description

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

## Usage

 ```1 2 3 4 5 6``` ```gpd.pfshape(fitted, range, xlab, ylab, conf = 0.95, nrang = 100, vert.lines = TRUE, ...) gpd.pfscale(fitted, range, xlab, ylab, conf = 0.95, nrang = 100, vert.lines = TRUE, ...) gpd.pfrl(fitted, prob, range, thresh, xlab, ylab, conf = 0.95, nrang = 100, vert.lines = TRUE, ...) ```

## Arguments

 `fitted` `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

 ```1 2 3 4 5 6 7``` ```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)) ```

### Example output  ```Warning message:
In clust(ardieres, u = 4, tim.cond = 8/365, clust.max = TRUE) :
NA's are not allowed in object ``data''.
Replacing them by -1e6 !!!
If there is some troubles try to put vert.lines = FALSE or change
the range...
conf.inf   conf.sup
0.09292929 0.54545455
npy retper prob
1   2     10 0.95
If there is some troubles try to put vert.lines = FALSE or change
the range...
conf.inf conf.sup
12.85354 20.60101
```

POT documentation built on May 2, 2019, 7:30 a.m.