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library(serocalculator)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
set.seed(1)
n = 480
lambda = 0.036
age = runif(n = n, min = 0, max = 80)
S1 = S2 = rep(0, n)

for (i in 1:n)
{
  a = 0
  while(S2[i] < age[i])
  {
    delta = rexp(n = 1, rate = lambda)
    S2[i] = S2[i] + delta
  }
  
  S1[i] = S2[i] - delta
  
  
}

data = tibble(
  age,
  S1,
  S2,
  W = S2 - S1,
  T1 = age - S1,
  `min(W,age)` = min(W, age),
  rel = T1/`min(W,age)`
  
)

hist(data$T1, breaks = 50)

hist(data$rel, breaks = 50)