GPDresiduals: GPD residual plot

In TReynkens/ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

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.

Author(s)

Tom Reynkens

References

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

See Also

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
pot <- GPDmle(SOAdata, plot=TRUE)

# Residual plot
k <- 200
GPDresiduals(SOAdata, sort(SOAdata)[length(SOAdata)-k], pot$gamma[k], pot$sigma[k])

TReynkens/ReIns documentation built on Nov. 9, 2023, 1:29 p.m.