dmnts: dmnts

In aaron9011/temStaR-v0.814: Tempered Stable Distribution

Description

dmnts calculates the density of the multivariate NTS distribution: f(x_1, \cdots, x_n)=\frac{d^n}{dx_1\cdots dx_n}P(x_n<R_1, \cdots, x_n<R_n). The multivariate NTS random vector R = (R_1, \cdots, R_n) is defined

R = μ + diag(σ) X,

where

X follows stdNTS_n(α, θ, β, Σ)

Usage

dmnts(x, st, subTS = NULL)

Arguments

x	array of the (x_1, \cdots, x_n)
st	Structure of parameters for the n-dimensional NTS distribution. st$ndim : dimension st$mu : μ mean vector (column vector) of the input data. st$sigma : σ standard deviation vector (column vector) of the input data. st$alpha : α of the std NTS distribution (X). st$theta : θ of the std NTS distribution (X). st$beta : β vector (column vector) of the std NTS distribution (X). st$Rho : ρ matrix of the std NTS distribution (X).
numofsample	number of samples.

Value

Simulated NTS random vectors

References

Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk https://arxiv.org/pdf/2007.13972.pdf

Examples

library("temStaR")
library(mvtnorm)
strPMNTS <- list(ndim = 2,
              mu = c( 0.5, -1.5 ),
              sigma = c( 2, 3 ),
              alpha = 0.1,
              theta = 3,
              beta =  c( 0.1, -0.3 ),
              Rho = matrix( data = c(1.0, 0.75, 0.75, 1.0),
                            nrow = 2, ncol = 2)
)
dmnts(c(0.6, -1.0), st = strPMNTS)


strPMNTS <- list(ndim = 2,
                 mu = c( 0, 0, 0 ),
                 sigma = c( 1, 1, 1 ),
                 alpha = 0.1,
                 theta = 3,
                 beta =  c( 0.1, -0.3, 0 ),
                 Rho = matrix(
                     data = c(1.0, 0.75, 0.1, 0.75, 1.0, 0.2, 0.1, 0.2, 1.0),
                     nrow = 3, ncol = 3)
)
pmnts(c(0,0,0), st = strPMNTS)
dmnts(c(0,0,0), st = strPMNTS)

aaron9011/temStaR-v0.814 documentation built on Dec. 24, 2021, 6:16 p.m.