qq is a generic function used to show quantile-quantile plot.
The function invokes particular methods
which depend on the class of the first argument.
So the function makes a quantile quantile plot for univariate POT models.
qq(object, ...)# S3 method for uvpot
qq(object, main, xlab, ylab, ci = TRUE, ...)
A graphical window.
A fitted object. When using the POT package, an object
of class 'uvpot'. Most often, the
return of the fitgpd function.
The title of the graphic. If missing, the title is set to
"QQ-plot".
The labels for the x and y axis. If missing, they are
set to "Model" and "Empirical" respectively.
Logical. If TRUE (the default), 95% intervals are
plotted.
Other arguments to be passed to the plot
function.
Mathieu Ribatet
The quantile quantile plot consists of plotting the observed quantiles in function of the theoretical ones. The theoretical quantiles \(Q_{Theo, j}\) are computed from the fitted GPD, that is:
$$Q_{Theo, j} = F^{-1}(p_j)$$ where \(F^{-1}\) is the fitted quantile function and \(p_j\) are empirical probabilities defined by :
$$p_{j:n} = \frac{j - 0.35}{n}$$ where \(n\) is the total number of observations - see Hosking (1995).
If the theoretical model is correct, then points should be ``near'' the line \(y=x\).
Hosking, J. R. M. and Wallis, J. R. (1995). A comparison of unbiased and plotting-position estimators of L moments. Water Resources Research. 31(8): 2019--2025.
qq, qq.uvpot
x <- rgpd(75, 1, 2, 0.1)
pwmu <- fitgpd(x, 1, "pwmu")
qq(pwmu)
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