ExtremalDep (version 1.0.0)

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

Description

Empirical estimation of 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)

Value

A list containing:

model

The specified model.

n

Number of random generations.

dep

Dependence parameter.

data

Input dataset.

Aest

Estimated Pickands dependence function.

hest

Estimated angular density.

Hest

Estimated angular measure.

p0,p1

Point masses at the edge of the simplex.

wsim

Simulated sample from the angular density.

Atrue,htrue

True Pickands dependence function and angular density, if model is specified.

Arguments

data

The dataset in vector form.

model

A character string specifying the model. Must be one of: "log", "alog", "hr", "neglog", "aneglog", "bilog", "negbilog", "ct", "amix", "Extremalt".

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 for asymmetry parameters, required for asymmetric logistic (model = 'alog') and asymmetric negative logistic (model = 'aneglog') models.

alpha,beta

Parameters for the bilogistic, negative bilogistic, Coles-Tawn, and asymmetric mixed models.

df

The degrees of freedom for the Extremal-t model.

seed

Seed for data generation. Required if data = NULL.

k

The polynomial order.

nsim

The number of generations from the estimated angular density.

plot

Logical; if TRUE, plots the fitted angular density, histogram of generated observations, and true angular density (if model is specified).

nw

The number of points at which the estimated functions are evaluated.

Author

Simone Padoan, , https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, , https://www.borisberanger.com; Giulia Marcon,

Details

See Marcon et al. (2017) for details.

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 correspond to left panels
# of Figures 1, 2 & 3 from Marcon et al. (2017)
################################################

## Figure 1 - symmetric logistic
# \donttest{
# 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
# \donttest{
# Strong dependence
d <- angular(model = 'alog', n = 25, dep = 0.3,
             asy = c(0.3,0.8), seed = 43121465, k = 20, nsim = 10000)
# Mild dependence
e <- angular(model = 'alog', n = 25, dep = 0.6,
             asy = c(0.3,0.8), seed = 1890, k = 10, nsim = 10000)
# Weak dependence
f <- angular(model = 'alog', n = 25, dep = 0.9,
             asy = c(0.3,0.8), seed = 2043, k = 5, nsim = 10000)
# }