dnts: dnts

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

dnts

Description

dnts calculates pdf of the NTS distribution with parameters (\alpha, \theta, \beta, \gamma, \mu). If only three parameters are given, it calculates pdf of the standard NTS distribution with parameter (\alpha, \theta, \beta) If a time parameter value is given, it calculates pdf of the NTS profess f(x)dx=d(P((X(t+s)-X(s))<x)), where X is the NTS process generated by the NTS distribution with parameters (\alpha, \theta, \beta, \gamma, \mu).

Usage

dnts(xdata, ntsparam)

Arguments

xdata	An array of x
ntsparam	A vector of the NTS parameters (\alpha, \theta, \beta, \gamma, \mu). For the NTS process case it is a vector of parameters (\alpha, \theta, \beta, \gamma, \mu, t). A vector of the standard NTS parameters (\alpha, \theta, \beta).

Value

Density of NTS distribution

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(functional)
library(nloptr)
library(pracma)
library(spatstat)
library(Matrix)
library("temStaR")

alpha <- 1.2
theta <- 1
beta <- -0.2
ntsparam <- c(alpha, theta, beta)
x <- seq(from = -6, to = 6, length.out = 101)
d <- dnts(x, ntsparam)
plot(x,d,type = 'l')

alpha <- 1.2
theta <- 1
beta <- -0.2
gamma <- 0.3
mu <- 0.1
ntsparam <- c(alpha, theta, beta, gamma, mu)
x <- seq(from = -2, to = 2, by = 0.01)
d <- dnts(x, ntsparam)
plot(x,d,type = 'l')


#Annual based parameters
alpha <- 1.2
theta <- 1
beta <- -0.2
gamma <- 0.3
mu <- 0.1
#scaling annual parameters to one day
dt <- 1/250 #one day
ntsparam <- c(alpha, theta, beta, gamma, mu, dt)
x <- seq(from = -0.02, to = 0.02, length.out = 101)
d <- dnts(x, ntsparam)
plot(x,d,type = 'l')

aaron9011/temStaR-v0.90 documentation built on June 1, 2025, 4:15 p.m.