dmnts: dmnts

In aaron9011/temStaR-v0.90: Tempered Stable Distribution

dmnts

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 = \mu + diag(\sigma) X,

where

X follows stdNTS_n(\alpha, \theta, \beta, \Sigma)

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 : \mu mean vector (column vector) of the input data. st$sigma : \sigma standard deviation vector (column vector) of the input data. st$alpha : \alpha of the std NTS distribution (X). st$theta : \theta of the std NTS distribution (X). st$beta : \beta vector (column vector) of the std NTS distribution (X). st$Rho : \rho 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-v0.90 documentation built on June 1, 2025, 4:15 p.m.