dExtDep | R Documentation |
This function calculates the density of parametric multivariate extreme distributions and corresponding angular density, or the non-parametric angular density represented through Bernstein polynomials.
dExtDep(x, method="Parametric", model, par, angular=TRUE, log=FALSE,
c=NULL, vectorial=TRUE, mixture=FALSE)
x |
A vector or a matrix. The value at which the density is evaluated. |
method |
A character string taking value |
model |
A string with the name of the model: |
par |
A vector representing the parameters of the (parametric or non-parametric) model. |
angular |
A logical value specifying if the angular density is computed. |
log |
A logical value specifying if the log density is computed. |
c |
A real value in |
vectorial |
A logical value; if |
mixture |
A logical value specifying if the Bernstein polynomial representation of distribution should be expressed as a mixture. If |
Note that when method="Parametric"
and angular=FALSE
, the density is only available in 2 dimensions.
When method="Parametric"
and angular=TRUE
, the models "AL"
, "ET"
and "EST"
are limited to 3 dimensions. This is because of the existence of mass on the subspaces on the simplex (and therefore the need to specify c
).
For the parametric models, the appropriate length of the parameter vector can be obtained from the dim_ExtDep
function and are summarized as follows.
When model="HR"
, the parameter vector is of length choose(dim,2)
.
When model="PB"
or model="Extremalt"
, the parameter vector is of length choose(dim,2) + 1
.
When model="EST"
, the parameter vector is of length choose(dim,2) + dim + 1
.
When model="TD"
, the parameter vector is of length dim
.
When model="AL"
, the parameter vector is of length 2^(dim-1)*(dim+2) - (2*dim+1)
.
If x
is a matrix and vectorial=TRUE
, a vector of length nrow(x)
, otherwise a scalar.
Simone Padoan, simone.padoan@unibocconi.it, https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com;
Beranger, B. and Padoan, S. A. (2015). Extreme dependence models, chapater of the book Extreme Value Modeling and Risk Analysis: Methods and Applications, Chapman Hall/CRC.
Beranger, B., Padoan, S. A. and Sisson, S. A. (2017). Models for extremal dependence derived from skew-symmetric families. Scandinavian Journal of Statistics, 44(1), 21-45.
Coles, S. G., and Tawn, J. A. (1991), Modelling Extreme Multivariate Events, Journal of the Royal Statistical Society, Series B (Methodological), 53, 377–392.
Cooley, D.,Davis, R. A., and Naveau, P. (2010). The pairwise beta distribution: a flexible parametric multivariate model for extremes. Journal of Multivariate Analysis, 101, 2103–2117.
Engelke, S., Malinowski, A., Kabluchko, Z., and Schlather, M. (2015), Estimation of Husler-Reiss distributions and Brown-Resnick processes, Journal of the Royal Statistical Society, Series B (Methodological), 77, 239–265.
Husler, J. and Reiss, R.-D. (1989), Maxima of normal random vectors: between independence and complete dependence, Statistics and Probability Letters, 7, 283–286.
Marcon, G., Padoan, S.A., Naveau, P., Muliere, P. and Segers, J. (2017) Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials. Journal of Statistical Planning and Inference, 183, 1-17.
Nikoloulopoulos, A. K., Joe, H., and Li, H. (2009) Extreme value properties of t copulas. Extremes, 12, 129–148.
Opitz, T. (2013) Extremal t processes: Elliptical domain of attraction and a spectral representation. Jounal of Multivariate Analysis, 122, 409–413.
Tawn, J. A. (1990), Modelling Multivariate Extreme Value Distributions, Biometrika, 77, 245–253.
pExtDep
, rExtDep
, fExtDep
, fExtDep.np
# Example of PB on the 4-dimensional simplex
dExtDep(x=rbind(c(0.1,0.3,0.3,0.3),c(0.1,0.2,0.3,0.4)), method="Parametric",
model="PB", par=c(2,2,2,1,0.5,3,4), log=FALSE)
# Example of EST in 2 dimensions
dExtDep(x=c(1.2,2.3), method="Parametric", model="EST", par=c(0.6,1,2,3), angular=FALSE, log=TRUE)
# Example of non-parametric angular density
beta <- c(1.0000000, 0.8714286, 0.7671560, 0.7569398,
0.7771908, 0.8031573, 0.8857143, 1.0000000)
dExtDep(x=rbind(c(0.1,0.9),c(0.2,0.8)), method="NonParametric", par=beta)
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