charStable: The characteristic function of a stable distribution

In gmm: Generalized Method of Moments and Generalized Empirical Likelihood

The characteristic function of a stable distribution

Description

It computes the theoretical characteristic function of a stable distribution for two different parametrizations. It is used in the vignette to illustrate the estimation of the parameters using GMM.

Usage

charStable(theta, tau, pm = 0)

Arguments

theta	Vector of parameters of the stable distribution. See details.
tau	A vector of numbers at which the function is evaluated.
pm	The type of parametization. It takes the values 0 or 1.

Details

The function returns the vector \Psi(\theta,\tau,pm) defined as E(e^{ix\tau}, where \tau is a vector of real numbers, i is the imaginary number, x is a stable random variable with parameters \theta = (\alpha,\beta,\gamma,\delta) and pm is the type of parametrization. The vector of parameters are the characteristic exponent, the skewness, the scale and the location parameters, respectively. The restrictions on the parameters are: \alpha \in (0,2], \beta\in [-1,1] and \gamma>0. For mode details see Nolan(2009).

Value

It returns a vector of complex numbers with the dimension equals to length(tau).

References

Nolan J. P. (2020), Univariate Stable Distributions - Models for Heavy Tailed Data. Springer Series in Operations Research and Financial Engineering. URL https://edspace.american.edu/jpnolan/stable/.

Examples

# GMM is like GLS for linear models without endogeneity problems

pm <- 0
theta <- c(1.5,.5,1,0) 
tau <- seq(-3, 3, length.out = 20)
char_fct <- charStable(theta, tau, pm)

gmm documentation built on June 7, 2023, 6:05 p.m.