| acf_DExp {trawl} | R Documentation |
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 |
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.
Value
The autocorrelation function of the double exponential trawl function evaluated at x
Examples
acf_DExp(1,0.3,0.1,2)