GPDresiduals function

GPD residual plot

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

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

when $\gamma \neq 0$ and

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.

Returns

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.

References

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

Author(s)

Tom Reynkens

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])