acf_DExp() R function from [trawl]

Autocorrelation function of the double exponential trawl function

This function computes the autocorrelation function associated with the double exponential trawl function.


acf_DExp(x, w, lambda1, lambda2)

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

The autocorrelation function of the double exponential trawl function evaluated at x

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_1x}+(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.


acf_DExp(1,0.3,0.1,2)

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