dmesn {ExtremalDep}

Bivariate and trivariate extended skew-normal distribution

Description

Density function, distribution function for the bivariate and trivariate extended skew-normal (ESN) distribution.

Usage

dmesn(x=c(0,0), location=rep(0, length(x)), scale=diag(length(x)),
      shape=rep(0,length(x)), extended=0)
pmesn(x=c(0,0), location=rep(0, length(x)), scale=diag(length(x)),
      shape=rep(0,length(x)), extended=0)

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.

Value

density (dmesn), probability (pmesn) from the bivariate or trivariate extended skew-normal distribution with given location, scale, shape and extended parameters or from the skew-normal distribution if extended=0. If shape=0 and extended=0 then the normal 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. (1999). Statistical applications of the multivariate skew normal distribution. J.Roy.Statist.Soc. B 61, 579–602.

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

Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715–726.

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

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


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