which) are currently provided:
a P-P plot, a Q-Q plot, a density plot and a return level plot.## S3 method for class 'uvevd':
plot(x, which = 1:4, main = c("Probability Plot",
"Quantile Plot", "Density Plot", "Return Level Plot"),
ask = nb.fig < length(which) && dev.interactive(),
ci = TRUE, adjust = 1, jitter = FALSE, nplty = 2, ...)"uvevd".1:4.TRUE, the user is asked before
each plot.TRUE (the default), plot simulated
95% confidence intervals for the P-P, Q-Q and return level
plots.adjust controls the smoothing bandwidth for the
non-parametric estimate (see < The P-P plot consists of the points
$${(G_n(z_i), G(z_i)), i = 1,\ldots,m}$$
where $G_n$ is the empirical distribution function
(defined using ppoints), G is the model based
estimate of the distribution (generalized extreme value
or generalized Pareto), and $z_1,\ldots,z_m$ are the data
used in the fitted model, sorted into ascending order.
The Q-Q plot consists of the points
$${(G^{-1}(p_i), z_i), i = 1,\ldots,m}$$
where $G^{-1}$ is the model based estimate of the quantile
function (generalized extreme value or generalized Pareto),
$p_1,\ldots,p_m$ are plotting points defined by
ppoints, and $z_1,\ldots,z_m$ are the data
used in the fitted model, sorted into ascending order.
The return level plot for generalized extreme value models is defined as follows. Let $G$ be the generalized extreme value distribution function, with location, scale and shape parameters $a$, $b$ and $s$ respectively. Let $z_t$ be defined by $G(z_t) = 1 - 1/t$. In common terminology, $z_t$ is the return level associated with the return period $t$.
Let $y_t = -1/\log(1 - 1/t)$. It follows that $$z_t = a + b(y_t^s - 1)/s.$$ When $s = 0$, $z_t$ is defined by continuity, so that $$z_t = a + b\log(y_t).$$ The curve within the return level plot is $z_t$ plotted against $y_t$ on a logarithmic scale, using maximum likelihood estimates of $(a,b,s)$. If the estimate of $s$ is zero, the curve will be linear. For large values of $t$, $y_t$ is approximately equal to the return period $t$. It is usual practice to label the x-axis as the return period.
The points on the plot are
$${(-1/\log(p_i), z_i), i = 1,\ldots,m}$$
where $p_1,\ldots,p_m$ are plotting points defined by
ppoints, and $z_1,\ldots,z_m$ are the data
used in the fitted model, sorted into ascending order.
For a good fit the points should lie ``close'' to the curve.
The return level plot for peaks over threshold models is
defined as follows.
Let $G$ be the generalized Pareto distribution function,
with location, scale and shape parameters $u$, $b$
and $s$ respectively, where $u$ is the model threshold.
Let $z_m$ denote the $m$ period return level
(see fpot and the notation therein).
It follows that
$$z_m = u + b((pmN)^s - 1)/s.$$
When $s = 0$, $z_m$ is defined by continuity, so that
$$z_m = u + b\log(pmN).$$
The curve within the return level plot is $z_m$ plotted
against $m$ on a logarithmic scale, using maximum likelihood
estimates of $(b,s,p)$. If the estimate of $s$ is zero,
the curve will be linear.
The points on the plot are
$${(1/(pN(1-p_i)), z_i), i = 1,\ldots,m}$$
where $p_1,\ldots,p_m$ are plotting points defined by
ppoints, and $z_1,\ldots,z_m$ are the data
used in the fitted model, sorted into ascending order.
For a good fit the points should lie ``close'' to the curve.
plot.bvevd, density,
jitter, rug, ppointsuvdata <- rgev(100, loc = 0.13, scale = 1.1, shape = 0.2)
M1 <- fgev(uvdata)
par(mfrow = c(2,2))
plot(M1)
uvdata <- rgpd(100, loc = 0, scale = 1.1, shape = 0.2)
M1 <- fpot(uvdata, 1)
par(mfrow = c(2,2))
plot(M1)Run the code above in your browser using DataLab