plot.uvevd {evd} | R Documentation

## 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 = 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, ...)

### 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.
`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.
`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.
`...` | 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,...,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,...,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,...,m}

where G^{-1} is the model based estimate of the quantile function (generalized extreme value or generalized Pareto), p_1,...,p_m are plotting points defined by `ppoints`, and z_1,...,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,...,m}

where p_1,...,p_m are plotting points defined by `ppoints`, and z_1,...,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,...,m}

where p_1,...,p_m are plotting points defined by `ppoints`, and z_1,...,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)

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