Probability of detection in a single grab sample

This function calculates the probability of detection in a single grab sample comprising of r primary increments for given serial correlation d.

prob_detect_single_grab(r, p, d)

Arguments

r

number of primary increments in a grab sample or grab sample size

p

limiting fraction or proportion of contaminated increments

d

serial correlation of contamination between the primary increments

Value

Probability of detection in a grab sample

Details

The probability of detection in any of the grab sample is given by \(p_d\) as $$p_d = 1-(1-p)(1-p(1-d))^{r-1}$$

Examples

   r <-  25
   p <-  0.005
   d <-  0.99
   prob_detect_single_grab(r, p, d)
#> [1] 0.006193314