dmest {ExtremalDep}

Bivariate and trivariate extended skew-t distribution

Description

Density function, distribution function for the bivariate and trivariate extended skew-t (EST) distribution.

Usage

dmest(x=c(0,0), location=rep(0, length(x)), scale=diag(length(x)),
      shape=rep(0,length(x)), extended=0, df=Inf)
pmest(x=c(0,0), location=rep(0, length(x)), scale=diag(length(x)),
      shape=rep(0,length(x)), extended=0, df=Inf)

Arguments

x

quantile vector of length d=2 or d=3.

location

a numeric location vector of length d. 0 is the default.

scale

a symmetric positive-definite scale matrix of dimension (d,d). diag(d) is the default.

shape

a numeric skewness vector of length d. 0 is the default.

extended

a single value extension parameter. 0 is the default.

df

a single positive value representing the degree of freedom; it can be non-integer. Default value is nu=Inf which corresponds to the skew-normal distribution.

Value

density (dmest), probability (pmest) from the bivariate or trivariate extended skew-t distribution with given location, scale, shape, extended and df parameters or from the skew-t distribution if extended=0. If shape=0 and extended=0 then the t distribution is recovered.

Author(s)

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

References

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J.Roy. Statist. Soc. B 65, 367–389.

Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monograph series.

Examples

sigma1 <- matrix(c(2,1.5,1.5,3),ncol=2)
sigma2 <- matrix(c(2,1.5,1.8,1.5,3,2.2,1.8,2.2,3.5),ncol=3)
shape1 <- c(1,2)
shape2 <- c(1,2,1.5)

dens1 <- dmest(x=c(1,1), scale=sigma1, shape=shape1, extended=2, df=1)
dens2 <- dmest(x=c(1,1), scale=sigma1, df=1)
dens3 <- dmest(x=c(1,1,1), scale=sigma2, shape=shape2, extended=2, df=1)
dens4 <- dmest(x=c(1,1,1), scale=sigma2, df=1)

prob1 <- pmest(x=c(1,1), scale=sigma1, shape=shape1, extended=2, df=1)
prob2 <- pmest(x=c(1,1), scale=sigma1, df=1)


prob3 <- pmest(x=c(1,1,1), scale=sigma2, shape=shape2, extended=2, df=1)
prob4 <- pmest(x=c(1,1,1), scale=sigma2, df=1)