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Version 2.3.1 (2006-06-01)
ISBN 3-900051-07-0

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> 
>  library(aster)
Loading required package: trust
> 
>  alpha <- 2.222
>  k <- 2
>  ifam <- fam.truncated.negative.binomial(alpha, k)
>  aster:::setfam(list(ifam))
>  aster:::getfam()
[[1]]
[[1]]$name
[1] "truncated.negative.binomial"

[[1]]$size
[1] 2.222

[[1]]$truncation
[1] 2

[[1]]$origin
[1] -1


>  aster:::clearfam()
> 
>  ##### 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
>  beeta <- pnbinom(k + 1, size = alpha, prob = pp, lower.tail = FALSE) /
+      dnbinom(k + 1, size = alpha, prob = pp)
> 
>  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)) +
+      pnbinom(k, size = alpha, prob = pp, lower.tail = FALSE, log.p = TRUE))
[1] TRUE
>  all.equal(first, alpha * qq / pp + (k + 1) / (1 + beeta) / pp)
[1] TRUE
>  all.equal(second, alpha * qq / pp^2 - (k + 1) / (1 + beeta) / pp^2 *
+      (- qq + (k + 1 + alpha) * qq / (1 + beeta) +
+      (alpha - pp * (k + 1 + alpha)) * beeta / (1 + beeta)))
[1] TRUE
> 
>  ##### usual size theta (continued) #####
>  ##### check by numerical derivative #####
> 
>  epsilon <- 1e-8
> 
>  zeroth.minus <- zeroth
>  zeroth.plus <- zeroth
>  for (i in seq(along = theta)) {
+      zeroth.minus[i] <- famfun(ifam, 0, theta[i] - epsilon)
+      zeroth.plus[i] <- famfun(ifam, 0, theta[i] + epsilon)
+  }
>  all.equal(first, (zeroth.plus - zeroth.minus) / (2 * epsilon),
+      tolerance = sqrt(epsilon))
[1] TRUE
> 
>  first.minus <- first
>  first.plus <- first
>  for (i in seq(along = theta)) {
+      first.minus[i] <- famfun(ifam, 1, theta[i] - epsilon)
+      first.plus[i] <- famfun(ifam, 1, theta[i] + epsilon)
+  }
>  all.equal(second, (first.plus - first.minus) / (2 * epsilon),
+      tolerance = sqrt(epsilon))
[1] TRUE
> 
>  ##### very large negative theta #####
> 
>  rm(p)
> 
>  theta <- seq(-100, -10, 10)
>  qq <- exp(theta)
>  pp <- (- expm1(theta))
>  beeta.up <- pnbinom(k + 1, size = alpha, prob = pp, lower.tail = FALSE)
>  beeta.dn <- dnbinom(k + 1, size = alpha, prob = pp)
>  beeta <- beeta.up / beeta.dn
>  beeta[beeta.up == 0] <- 0
> 
>  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)) +
+      pnbinom(k, size = alpha, prob = pp, lower.tail = FALSE, log.p = TRUE))
[1] TRUE
>  all.equal(first, alpha * qq / pp + (k + 1) / (1 + beeta) / pp)
[1] TRUE
>  all.equal(second, alpha * qq / pp^2 - (k + 1) / (1 + beeta) / pp^2 *
+      (- qq + (k + 1 + alpha) * qq / (1 + beeta) +
+      (alpha - pp * (k + 1 + alpha)) * beeta / (1 + beeta)))
[1] TRUE
> 
>  ##### very small negative theta #####
> 
>  theta <- (- 10^(- c(1:9, seq(10, 100, 10))))
>  qq <- exp(theta)
>  pp <- (- expm1(theta))
>  beeta <- pnbinom(k + 1, size = alpha, prob = pp, lower.tail = FALSE) /
+      dnbinom(k + 1, size = alpha, prob = pp)
> 
>  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)) +
+      pnbinom(k, size = alpha, prob = pp, lower.tail = FALSE, log.p = TRUE))
[1] TRUE
>  all.equal(first, alpha * qq / pp + (k + 1) / (1 + beeta) / pp)
[1] TRUE
>  all.equal(second, alpha * qq / pp^2 - (k + 1) / (1 + beeta) / pp^2 *
+      (- qq + (k + 1 + alpha) * qq / (1 + beeta) +
+      (alpha - pp * (k + 1 + alpha)) * beeta / (1 + beeta)))
[1] TRUE
> 
>  ##### random #####
> 
>  nind <- 50
>  theta <- rep(- 1.75, nind)
>  pred <- 0 
>  fam <- 1
>  root <- rep(1:3, length.out = nind)
>  theta <- cbind(theta)
>  root <- cbind(root)
>  qq <- exp(theta)
>  pp <- (- expm1(theta))
>  mu <- alpha * qq / pp
>     
>  set.seed(42)
>  rout <- raster(theta, pred, fam, root, famlist = list(ifam))
>  
>  set.seed(42)
>  rout.too <- rktnb(nind, alpha, k, mu, root)
>  
>  all.equal(as.numeric(rout), rout.too)
[1] TRUE
> 
>