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 0w10\le w\le 1 and λ1,λ2>0\lambda_1, \lambda_2 > 0 as follows:

g(x)=weλ1x+(1w)eλ2x,\mboxforx0.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)=(weλ1x/λ1+(1w)eλ2x/λ2)/c,\mboxforx0,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/λ1+(1w)/λ2.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)

[Package trawl version 0.2.2 Index]