R version 3.5.1 (2018-07-02) -- "Feather Spray"
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Platform: x86_64-pc-linux-gnu (64-bit)

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> 
>  library(aster)
Loading required package: trust
> 
>  ifam <- fam.truncated.poisson(truncation = 0)
> 
>  # change to include all cases in case splitting
>  # see ../src/astfam.c lines 338 to 373
>  theta <- seq(-6, 6, 0.5)
>  mu <- exp(theta)
> 
>  zeroth <- double(length(theta))
>  first <- double(length(theta))
>  second <- double(length(theta))
> 
>  for (i in seq(along = theta)) {
+     zeroth[i] <- famfun(ifam, 0, theta[i])
+     first[i] <- famfun(ifam, 1, theta[i])
+     second[i] <- famfun(ifam, 2, theta[i])
+  }
> 
>  all.equal(zeroth, log(exp(mu) - 1))
[1] TRUE
>  tau <- mu / (1 - exp(- mu))
>  all.equal(first, tau)
[1] TRUE
>  all.equal(second, tau * (1 - tau * exp(- mu)))
[1] TRUE
> 
> 
> proc.time()
   user  system elapsed 
  0.248   0.012   0.250