# GPDresiduals: GPD residual plot In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

 GPDresiduals R Documentation

## GPD residual plot

### Description

Residual plot to check GPD fit for peaks over a threshold.

### Usage

GPDresiduals(data, t, gamma, sigma, plot = TRUE,
main = "GPD residual plot", ...)


### Arguments

 data Vector of n observations. t The used threshold. gamma Estimate for the EVI obtained from GPDmle. sigma Estimate for \sigma obtained from GPDmle. plot Logical indicating if the residuals should be plotted, default is FALSE. main Title for the plot, default is "GPD residual plot". ... Additional arguments for the plot function, see plot for more details.

### Details

Consider the POT values Y=X-t and the transformed variable

R= 1/\gamma \log(1+\gamma/\sigma Y),

when \gamma \neq 0 and

R = Y/\sigma,

otherwise. We can assess the goodness-of-fit of the GPD when modelling POT values Y=X-t by constructing an exponential QQ-plot of the transformed variable R since R is standard exponentially distributed if Y follows the GPD.

See Section 4.2.2 in Albrecher et al. (2017) for more details.

### Value

A list with following components:

 res.the Vector of the theoretical quantiles from a standard exponential distribution. res.emp Vector of the empirical quantiles of R, see Details.

Tom Reynkens

### References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

GPDfit, ExpQQ

### Examples

data(soa)

# Look at last 500 observations of SOA data
SOAdata <- sort(soa$size)[length(soa$size)-(0:499)]

# Plot POT-MLE estimates as a function of k
GPDresiduals(SOAdata, sort(SOAdata)[length(SOAdata)-k], pot$gamma[k], pot$sigma[k])