Distributions function

Distributions of the GAS package

Density, distribution function, quantile function, random generator, moments, scores and information matrix of univariate and multivariate distributions of the GAS package.

ddist_Uni(y, Theta, Dist, log = FALSE)
pdist_Uni(q, Theta, Dist)
qdist_Uni(p, Theta, Dist)
rdist_Uni(Theta, Dist)
mdist_Uni(Theta, Dist)
Score_Uni(y, Theta, Dist)
IM_Uni(Theta, Dist)

ddist_Multi(y, Theta, Dist, log = FALSE)
rdist_Multi(Theta, N, Dist)
Score_Multi(y, Theta, Dist)

Arguments

• y, q: numeric Scalar quantile. For Score_Multi and ddist_Multi, y is a numeric vector.

• p: numeric Scalar probability.

• Theta: numeric Vector of distribution parameters. The order of the parameters is generally: location, scale, skewness, shape, shape2. When the distribution defined by Dist does not have, say, the shape parameter, this should be simply omitted. See also DistInfo for specific distributions.

• Dist: character Label of the conditional distribution, see DistInfo .

• log: logical If TRUE, the density value $p(y)$ is given as $log(p(y))$. Dy Default log = FALSE.

• N: numeric Integer. cross-sectional dimension for the multivariate case.

Details

The function mdist_Uni returns a vector with four elements: mean, variance, skewness

and kurtosis coefficients. The functions Score_Uni and IM_Uni returns the score and the Fisher information matrix for univariate distributions. The function Score_Multi returns the score for multivariate distributions. See DistInfo for the lists of supported distributions. These functions are not vectorized. ddist_Uni and ddist_Multi give the density, pdist_Uni gives the distribution function, qdist_Uni gives the quantile function, and rdist_Uni and rdist_Multi generate random deviates.

Returns

1. numeric scalar for: ddist_Uni, pdist_Uni, qdist_Uni, rdist_Uni,
2. numeric vector for: Score_Uni, Score_Multi and rdist_Multi,
3. matrix for IM_Uni.

Author(s)

Leopoldo Catania

Examples

# Skew Student-t distribution

# log density
Theta = c("location" = 0, "scales" = 1, "skewness" = 1.2, "shape" = 7)

ddist_Uni(y = 0.5, Theta, "sstd", TRUE)

# probability
pdist_Uni(q = -1.69, Theta, "sstd")

#quantile
qdist_Uni(p = 0.05, Theta, "sstd")

#random generator
rdist_Uni(Theta, "sstd")

#moments
mdist_Uni(Theta, "sstd")