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### Function to calculate an effective range for the distribution function
### or for the density function of the Hyperbolic Distribution
### DJS 8/09/06
hyperbCalcRange <- function(Theta, tol = 10^(-5), density = FALSE)
{
Theta <- as.numeric(Theta)
hyperbPi <- Theta[1]
zeta <- Theta[2]
delta <- Theta[3]
mu <- Theta[4]
KNu <- besselK(zeta, nu = 1)
phi <- as.numeric(hyperbChangePars(1, 3, Theta)[1])
gamma <- as.numeric(hyperbChangePars(1, 3, Theta)[2])
alpha <- (phi + gamma)/2
const <- 1/(2*delta*(1 + hyperbPi^2)^(1/2)*KNu)
## this shouldn't make a difference but is put in
## to follow the theory
tol <- min(tol, const/gamma, const/phi)
if (density == FALSE){
## bounds are for distribution function
xLower <- min(mu - (1/phi)*log(const/(tol*phi)), mu - delta)
xUpper <- max(mu + (1/gamma)*log(const/(tol*gamma)), mu + delta)
range <- c(xLower, xUpper)
}else{
## bounds are for the density function
xLower <- min(mu - 1/phi*log(const/tol), mu - delta)
xUpper <- max(mu + 1/gamma*log(const/tol), mu + delta)
range <- c(xLower, xUpper)
}
return(range)
} ## End of hyperbCalcRange()
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