Multivariate Product Distributions for Elliptically Contoured Distributions

Estimates multivariate subgaussian stable densities and probabilities as well as generates random variates using product distribution theory. A function for estimating the parameters from data to fit a distribution to data is also provided, using the method from Nolan (2013) .

mvpd: An R Package for Multivariate Product Distributions

• [dpr]mvss: multivariate subgaussian stable distributions
• [pr]mvlogis: multivariate logistic distributions

The goal of mvpd is to use product distribution theory to allow the numerical calculations of specific scale mixtures of the multivariate normal distribution. The multivariate subgaussian stable distribution is the product of the square root of a univariate positive stable distribution and the multivariate normal distribution (see Nolan (2013)).

Example

Generate 1000 draws from a random bivariate subgaussian stable distribution with alpha=1.71 and plot.

library(mvpd)
set.seed(2)
## basic example code
biv <- rmvss(n=1e3, alpha=1.71, Q=matrix(c(10,7.5,7.5,10),2))
head(biv)
#>             [,1]      [,2]
#> [1,]  3.17465324  4.122869
#> [2,] -3.26707008 -1.366920
#> [3,] -5.82800100  1.831774
#> [4,] -2.02463359 -3.749701
#> [5,]  0.01294963  3.042960
#> [6,]  1.73029594  3.812420
plot(biv); abline(h=0,v=0)