plot.bbeed {ExtremalDep}

R Documentation

Plot of Extremal Dependence

Description

Produces one or more plots of the extremal dependence.

Usage

## S3 method for class 'bbeed'
plot(x, type = c("summary", "returns", "A", "h", "pm", "k"),
          mcmc, summary.mcmc, nsim, burn, y, probs, CEX=1.5, A_true, h_true,
          labels=c(expression(y[1]),expression(y[2])), ...)

Arguments

x	Vector on the unit simplex where the dependence function is evaluated.
type	String, denoting the type of function to plot (see Details).
mcmc	The output of the bbeed function.
summary.mcmc	The output of the summary.bbeed function.
nsim	The number of simulation in the mcmc algorithm.
burn	The burn-in period.
y	A 2-column matrix of unobserved thresholds at which the returns are calculated. Required when type="y".
probs	The probability of joint exceedances, the output of the return function.
A_true	The true pickands dependence function (evaluated at x).
h_true	The true angular density function (evaluated at x).
CEX	Label and axis sizes.
labels	Labels.
...	Additional graphical parameters. See plot function for details.

Details

If type="returns", a (contour) plot of the probabilities of exceedances for some threshold y is returned.
If type="A", a plot of the estimated Pickands dependence function is drawn. If A_true is specified the plot includes the true Pickands dependence function and a functional boxplot for the estimated function. If type="h", a plot of the estimated angular density function is drawn. If h_true is specified the plot includes the true angular density and a functional boxplot for the estimated function. If type="pm", a plot of the prior against the posterior for the mass at \{0\} is drawn. If type="k", a plot of the prior against the posterior for the polynomial degree k is drawn. If type="summary", a 2 by 2 plot with types "A", "h", "pm" and "k" is returned.

Author(s)

Simone Padoan, simone.padoan@unibocconi.it, https://mypage.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com/; Giulia Marcon, giuliamarcongm@gmail.com

References

Marcon, G., Padoan, S.A., Naveau, P., Muliere, P., Segers, J. (2017) Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials. Journal of Statistical Planning and Inference, 183, 1-17.

See Also

beed.confband.

Examples

	if (interactive()){

	# This reproduces some of the results showed in Fig. 1 (Marcon, 2016).
	set.seed(1890)
	data <- evd::rbvevd(n=100, dep=.6, asy=c(0.8,0.3), model="alog", mar1=c(1,1,1))

	nsim = 500000
	burn = 400000

	mu.nbinom = 3.2
	var.nbinom = 4.48
	hyperparam <- list(a.unif=0, b.unif=.5, mu.nbinom=mu.nbinom, var.nbinom=var.nbinom)
	k0 = 5
	pm0 = list(p0=0.06573614, p1=0.3752118)
	eta0 = ExtremalDep:::rcoef(k0, pm0)

	mcmc <- bbeed(data, pm0, eta0, k0, hyperparam, nsim,
              prior.k = "nbinom", prior.pm = "unif")

	w <- seq(0.001, .999, length=100)
	summary.mcmc <- summary.bbeed(w, mcmc, burn, nsim, plot=TRUE)

	plot.bbeed(type = "A", x=w, mcmc=mcmc, summary.mcmc, nsim=nsim, burn=burn)
	plot.bbeed(type = "h", x=w, mcmc=mcmc, summary.mcmc, nsim=nsim, burn=burn)
	plot.bbeed(type = "pm", x=w, mcmc=mcmc, summary.mcmc, nsim=nsim, burn=burn)
	plot.bbeed(type = "k", x=w, mcmc=mcmc, summary.mcmc, nsim=nsim, burn=burn)

	Atrue <- evd::abvevd(w, dep=0.6, asy=c(0.3,0.8), model='alog')
	htrue <- evd::hbvevd(w, dep=0.6, asy=c(0.8,0.3), model='alog',half=TRUE)

	plot.bbeed(type = "A", summary.mcmc=summary.mcmc, A_true=Atrue)
	plot.bbeed(type = "h", summary.mcmc=summary.mcmc, h_true=htrue)

	}

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