ExtremalDep (version 1.0.0)

dest: Univariate extended skew-t distribution

Description

Density function, distribution function for the univariate extended skew-t (EST) distribution.

Usage

dest(x, location = 0, scale = 1, shape = 0, extended = 0, df = Inf)
pest(x, location = 0, scale = 1, shape = 0, extended = 0, df = Inf)

Value

density (dest), probability (pest) from the extended skew-t distribution with given

location, scale, shape, extended and df parameters or from the skew-t if extended = 0. If shape = 0 and extended = 0 then the t distribution is recovered.

Arguments

x

quantile.

location

location parameter. 0 is the default.

scale

scale parameter; must be positive. 1 is the default.

shape

skewness parameter. 0 is the default.

extended

extension parameter. 0 is the default.

df

a single positive value representing the degrees 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 Monographs series.

Examples

dens1 <- dest(x = 1, shape = 3, extended = 2, df = 1)
dens2 <- dest(x = 1, shape = 3, df = 1)
dens3 <- dest(x = 1, df = 1)
dens4 <- dt(x = 1, df = 1)
prob1 <- pest(x = 1, shape = 3, extended = 2, df = 1)
prob2 <- pest(x = 1, shape = 3, df = 1)
prob3 <- pest(x = 1, df = 1)
prob4 <- pt(q = 1, df = 1)