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", ...)data |
Vector of n observations. |
t |
The used threshold. |
gamma |
Estimate for the EVI obtained from |
sigma |
Estimate for σ obtained from |
plot |
Logical indicating if the residuals should be plotted, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
Consider the POT values Y=X-t and the transformed variable
R= 1/γ \log(1+γ/σ Y),
when γ \neq 0 and
R = Y/σ,
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.
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
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
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])
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