R Under development (unstable) (2023-12-13 r85679 ucrt) -- "Unsuffered Consequences"
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> 
>  library(aster)
> 
>  alpha <- 2.222
>  ifam <- fam.negative.binomial(alpha)
> 
>  ##### usual size theta #####
> 
>  p <- seq(0.9, 0.1, -0.1)
>  theta <- log(1 - p)
>  qq <- exp(theta)
>  pp <- (- expm1(theta))
>  all.equal(p, pp)
[1] TRUE
>  all.equal(pp, 1 - qq)
[1] TRUE
> 
>  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, alpha * (- log(pp)))
[1] TRUE
>  all.equal(first, alpha * qq / pp)
[1] TRUE
>  all.equal(second, alpha * qq / pp^2)
[1] TRUE
> 
>  ##### very large negative theta #####
> 
>  rm(p)
> 
>  theta <- seq(-100, -10, 10)
>  qq <- exp(theta)
>  pp <- (- expm1(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, alpha * (- log(pp)))
[1] TRUE
>  all.equal(first, alpha * qq / pp)
[1] TRUE
>  all.equal(second, alpha * qq / pp^2)
[1] TRUE
> 
>  ##### very small negative theta #####
> 
>  theta <- (- 10^(- c(1:9, seq(10, 100, 10))))
>  qq <- exp(theta)
>  pp <- (- expm1(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, alpha * (- log(pp)))
[1] TRUE
>  all.equal(first, alpha * qq / pp)
[1] TRUE
>  all.equal(second, alpha * qq / pp^2)
[1] TRUE
> 
>  ##### random #####
> 
>  nind <- 50
>  theta <- rep(- 1.75, nind)
>  pred <- 0
>  fam <- 1
>  root <- seq(1, by = 0.5, length = nind)
>  theta <- cbind(theta)
>  root <- cbind(root)
> 
>  set.seed(42)
>  rout <- raster(theta, pred, fam, root, famlist = list(ifam))
> 
>  set.seed(42)
>  rout.too <- rnbinom(nind, size = alpha * as.numeric(root),
+      prob = as.numeric(1 - exp(theta)))
> 
>  all.equal(as.numeric(rout), rout.too)
[1] TRUE
> 
> 
> 
> 
> proc.time()
   user  system elapsed 
   0.17    0.03    0.20