# bootCI: Pointwise confidence intervals by bootstrap In extremefit: Estimation of Extreme Conditional Quantiles and Probabilities

## Description

Pointwise quantiles and survival probabilities confidence intervals using bootstrap.

## Usage

 ```1 2 3 4``` ```bootCI(X, weights = rep(1, length(X)), probs = 1:(length(X) - 1)/length(X), xgrid = sort(X), B = 100, alpha = 0.05, type = "quantile", CritVal = 10, initprop = 1/10, gridlen = 100, r1 = 1/4, r2 = 1/20, plot = F) ```

## Arguments

 `X` a numeric vector of data values. `weights` a numeric vector of weights. `probs` used if type = "quantile", a numeric vector of probabilities with values in [0,1]. `xgrid` used if type = "survival", a numeric vector with values in the domain of X. `B` an integer giving the number of bootstrap iterations. `alpha` the type 1 error of the bootstrap (1-alpha)-confidence interval. `type` type is either "quantile" or "survival". `CritVal` a critical value associated to the kernel function given by `CriticalValue`. The default value is 10 corresponding to the rectangular kernel. `gridlen, initprop, r1, r2` parameters used in the function hill.adapt (see `hill.adapt`). `plot` If `TRUE`, the bootstrap confidence interval is plotted.

## Details

Generate B samples of X with replacement to estimate the quantiles of orders probs or the survival probability corresponding to xgrid. Determine the bootstrap pointwise (1-alpha)-confidence interval for the quantiles or the survival probabilities.

## Value

 `LowBound` the lower bound of the bootstrap (1-alpha)-confidence interval. `UppBound` the upper bound of the bootstrap (1-alpha)-confidence interval of level.

`hill.adapt`,`CriticalValue`,`predict.hill.adapt`
 ``` 1 2 3 4 5 6 7 8 9 10``` ```X <- abs(rcauchy(400)) hh <- hill.adapt(X) probs <- probgrid(0.1, 0.999999, length = 100) B <- 200 ## Not run: #For computing time purpose bootCI(X, weights = rep(1, length(X)), probs = probs, B = B, plot = TRUE) xgrid <- sort(sample(X, 100)) bootCI(X, weights = rep(1, length(X)), xgrid = xgrid, type = "survival", B = B, plot = TRUE) ## End(Not run) ```