This function calculates the resulting serial correlation between grab samples each having r primary increments with original serial correlation d.
correlation_grab(r, p, d)number of primary increments in a grab sample or grab sample size
limiting fraction or proportion of contaminated increments
serial correlation of contamination between the primary increments
Serial correlation between grab samples
The serial correlation between blocks (grab samples) is given by \(d_g\) as $$d_g = [dp(1-p(1-d))^{r-1}]/p_d$$ where \(p_d\) is the probability of detection in any of the block (grab sample) which is calculated by using prob_detect_single_grab.
r <- 25
p <- 0.005
d <- 0.99
correlation_grab(r, p, d)
#> [1] 0.7982905