acf_DExp: Autocorrelation function of the double exponential trawl function
Description
This function computes the autocorrelation function associated with the double
exponential trawl function.
Usage
acf_DExp(x, w, lambda1, lambda2)
Arguments
x
The argument (lag) at which the autocorrelation function associated
with the double exponential trawl function will be evaluated
w
parameter in the double exponential trawl
lambda1
parameter in the double exponential trawl
lambda2
parameter in the double exponential trawl
Value
The autocorrelation function of the double exponential trawl function
evaluated at x
Details
The trawl function is parametrised by parameters \(0\le w\le 1\)
and \(\lambda_1, \lambda_2 > 0\) as follows: $$g(x) = w e^{\lambda_1
x}+(1-w) e^{\lambda_2 x}, \mbox{ for } x \le 0.$$ Its autocorrelation
function is given by: $$r(x) = (w e^{-\lambda_1 x}/\lambda_1+(1-w)
e^{-\lambda_2 x}/\lambda_2)/c, \mbox{ for } x \ge 0,$$ where $$c =
w/\lambda_1+(1-w)/\lambda_2.$$