View source: R/Distributions.R
dmest | R Documentation |
Density function, distribution function for the bivariate and trivariate extended skew-t (EST) distribution.
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
)
x |
Quantile vector of length |
location |
A numeric location vector of length |
scale |
A symmetric positive-definite scale matrix of dimension
|
shape |
A numeric skewness vector of length |
extended |
A single value extension parameter.
|
df |
A single positive value representing the degree of freedom;
it can be non-integer. Default value is |
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.
Simone Padoan, simone.padoan@unibocconi.it, https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com;
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.
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)
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