ExtremalDep (version 1.0.0)

dmest: 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
)

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.

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.

Author

Simone Padoan, , https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, 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)

# \donttest{
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)
# }