angular {ExtremalDep}

Estimation of the angular density, angular measure and random generation from the angular distribution.

Description

Empirical estimation to the Pickands dependence function, the angular density, the angular measure and random generation of samples from the estimated angular density.

Usage

angular(data, model, n, dep, asy, alpha, beta, df, seed, k, nsim, plot=TRUE, nw=100)

Arguments

data

The dataset in vector form

model

The specified model; a character string. Must be either "log", "alog", "hr", "neglog", "aneglog", "bilog", "negbilog", "ct", "amix" or "Extremalt" for the logistic, asymmetric logistic, Husler-Reiss, negative logistic, asymmetric negative logistic, bilogistic, negative bilogistic, Coles-Tawn, asymetric mixed and Extremal-t models respectively.

n

The number of random generations from the model. Required if data=NULL.

dep

The dependence parameter for the model.

asy

A vector of length two, containing the two asymmetry parameters for the asymmetric logistic (model='alog') and asymmetric negative logistic models (model='aneglog').

alpha, beta

Alpha and beta parameters for the bilogistic, negative logistic, Coles-Tawn and asymmetric mixed models.

df

The degree of freedom for the extremal-t model.

seed

The seed for the data generation. Required if data=NULL.

k

The polynomial order.

nsim

The number of generations from the estimated angular density.

plot

If TRUE, the fitted angular density, histogram of the generated observations from the angular density and the true angular density (if model is specified) are displayed.

nw

The number of points at which the estimated functions are evaluated

Details

See Marcon et al. (2017).

Value

Returns a list which contains model, n, dep, data, Aest the estimated pickands dependence function, hest the estimated angular density, Hest the estimated angular measure, p0 and p1 the point masses at the edge of the simplex, wsim the simulated sample from the angular density and Atrue and htrue the true Pickand dependence function and angular density (if model is specified).

Author(s)

Simone Padoan, [e-mail], https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, [e-mail] https://www.borisberanger.com; Giulia Marcon, [e-mail]

References

Marcon, G., Naveau, P. and Padoan, S. A. (2017). A semi-parametric stochastic generator for bivariate extreme events, Stat 6(1), 184–201.

Examples

################################################
# The following examples provide the left panels
# of Figure 1, 2 & 3 of Marcon et al. (2017).
################################################

## Figure 1 - symmetric logistic


# Strong dependence
a <- angular(model='log', n=50, dep=0.3, seed=4321, k=20, nsim=10000)
# Mild dependence
b <- angular(model='log', n=50, dep=0.6, seed=212, k=10, nsim=10000)
# Weak dependence
c <- angular(model='log', n=50, dep=0.9, seed=4334, k=6, nsim=10000)


## Figure 2 - Asymmetric logistic


# Strong dependence
d <- angular(model='alog', n=25, dep=0.3, asy=c(.3,.8), seed=43121465, k=20, nsim=10000)
# Mild dependence
e <- angular(model='alog', n=25, dep=0.6, asy=c(.3,.8), seed=1890, k=10, nsim=10000)
# Weak dependence
f <- angular(model='alog', n=25, dep=0.9, asy=c(.3,.8), seed=2043, k=5, nsim=10000)