charStable {gmm}R Documentation

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^{ixtau}, where tau is a vector of real numbers, i is the imaginary number, x is a stable random variable with parameters theta = (α,β,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: α in (0,2], βin [-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. (2009), Stable Disttributions. Math/Stat Department, American University. URL http://academic2.american.edu/~jpnolan/stable/stable.html.

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)


[Package gmm version 1.3-0 Index]