plot.uvevd: Plot Diagnostics for a Univariate EVD Object

In evd: Functions for Extreme Value Distributions

Plot Diagnostics for a Univariate EVD Object

Description

Four plots (selectable by which) are currently provided: a P-P plot, a Q-Q plot, a density plot and a return level plot.

Usage

## S3 method for class 'uvevd'
plot(x, which = 1:4, main, ask = nb.fig <
    length(which) && dev.interactive(), ci = TRUE, cilwd = 1,
    a = 0, adjust = 1, jitter = FALSE, nplty = 2, ...)
## S3 method for class 'gumbelx'
plot(x, interval, which = 1:4, main, ask = nb.fig <
    length(which) && dev.interactive(), ci = TRUE, cilwd = 1,
    a = 0, adjust = 1, jitter = FALSE, nplty = 2, ...)

Arguments

x	An object that inherits from class "uvevd".
which	If a subset of the plots is required, specify a subset of the numbers 1:4.
main	Title of each plot. If given, must be a character vector with the same length as which.
ask	Logical; if TRUE, the user is asked before each plot.
ci	Logical; if TRUE (the default), plot simulated 95% confidence intervals for the P-P, Q-Q and return level plots.
cilwd	Line width for confidence interval lines.
a	Passed through to ppoints for empirical estimation. Larger values give less probability for extreme events.
adjust, jitter, nplty	Arguments to the density plot. The density of the fitted model is plotted with a rug plot and (optionally) a non-parameteric estimate. The argument adjust controls the smoothing bandwidth for the non-parametric estimate (see density). jitter is logical; if TRUE, the (possibly transformed) data are jittered to produce the rug plot. This need only be used if the data contains repeated values. nplty is the line type of the non-parametric estimate. To omit the non-parametric estimate set nplty to zero.
interval	A vector of length two, for the gumbelx (maximum of two Gumbels) model. This is passed to the uniroot function to calculate quantiles for the Q-Q and return level plots. The interval should be large enough to contain all plotted quantiles or an error from uniroot will occur.
...	Other parameters to be passed through to plotting functions.

Details

The following discussion assumes that the fitted model is stationary. For non-stationary generalized extreme value models the data are transformed to stationarity. The plot then corresponds to the distribution obtained when all covariates are zero.

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.

See Also

plot.bvevd, density, jitter, rug, ppoints

Examples

uvdata <- rgev(100, loc = 0.13, scale = 1.1, shape = 0.2)
M1 <- fgev(uvdata)
## Not run: par(mfrow = c(2,2))
## Not run: plot(M1)

uvdata <- rgpd(100, loc = 0, scale = 1.1, shape = 0.2)
M1 <- fpot(uvdata, 1)
## Not run: par(mfrow = c(2,2))
## Not run: plot(M1)

evd documentation built on Sept. 21, 2024, 9:06 a.m.