R Under development (unstable) (2023-12-13 r85679 ucrt) -- "Unsuffered Consequences"
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> 
>  library(aster)
>  library(numDeriv)
> 
>  do.chisq.test <- function(x, k, mu, max.bin) {
+      stopifnot(all(x > k))
+      stopifnot(k + 1 < max.bin)
+      xx <- seq(k + 1, max.bin)
+      yy <- dpois(xx, mu)
+      yy[length(yy)] <- ppois(max.bin - 1, mu, lower.tail = FALSE)
+      pp <- yy / sum(yy)
+      ecc <- length(x) * pp
+      if (any(ecc < 5.0))
+          warning("violates rule of thumb about > 5 expected in each cell")
+      cc <- tabulate(x, max.bin)
+      cc <- cc[xx]
+      cc[length(cc)] <- nsim - sum(cc[- length(cc)])
+      chisqstat <- sum((cc - ecc)^2 / ecc)
+      pval <- pchisq(chisqstat, length(ecc) - 1, lower.tail = FALSE)
+      if (exists("save.min.pval")) {
+          save.min.pval <<- min(pval, save.min.pval)
+          save.ntests <<- save.ntests + 1
+      } else {
+          save.min.pval <<- pval
+          save.ntests <<- 1
+      }
+      list(chisqstat = chisqstat, df = length(ecc) - 1, pval = pval,
+          observed = cc, expected = ecc, x = xx)
+  }
> 
>  set.seed(42)
>  nsim <- 1e4
> 
>  mu <- 10
>  k <- 2
>  x <- rktp(nsim, k, mu)
>  chisqout1 <- do.chisq.test(x, k, mu, 22)
> 
>  mu <- 3.5
>  k <- 2
>  x <- rktp(nsim, k, mu)
>  chisqout2 <- do.chisq.test(x, k, mu, 11)
> 
>  mu <- 2.5
>  k <- 2
>  x <- rktp(nsim, k, mu)
>  chisqout3 <- do.chisq.test(x, k, mu, 10)
> 
>  mu <- 1.5
>  k <- 2
>  x <- rktp(nsim, k, mu)
>  chisqout4 <- do.chisq.test(x, k, mu, 8)
> 
>  mu <- 0.5
>  k <- 2
>  x <- rktp(nsim, k, mu)
>  chisqout5 <- do.chisq.test(x, k, mu, 6)
> 
>  nsim <- 1e5
>  mu <- 0.1
>  k <- 2
>  x <- rktp(nsim, k, mu)
>  chisqout6 <- do.chisq.test(x, k, mu, 5)
> 
>  mu <- 0.01
>  k <- 2
>  x <- rktp(nsim, k, mu)
>  chisqout7 <- do.chisq.test(x, k, mu, 4)
> 
>  mu <- 1.5
>  xpred <- 0:10
>  save.seed <- .Random.seed
>  x <- rktp(xpred, k, mu, xpred)
>  .Random.seed <- save.seed
>  my.x <- rep(0, length(xpred))
>  for (i in seq(along = xpred))
+      if (xpred[i] > 0)
+          for (j in 1:xpred[i])
+              my.x[i] <- my.x[i] + rktp(1, k, mu)
>  all.equal(x, my.x)
[1] TRUE
> 
>  k <- 5
>  mu <- pi
>  x <- rktp(nsim, k, mu)
>  chisqout8 <- do.chisq.test(x, k, mu, 14)
> 
>  k <- 10
>  mu <- exp(2)
>  x <- rktp(nsim, k, mu)
>  chisqout9 <- do.chisq.test(x, k, mu, 22)
> 
>  cat("number of tests:", save.ntests, "\n")
number of tests: 9 
>  save.ntests * save.min.pval > 0.05
[1] TRUE
> 
>  #####
> 
>  set.seed(42)
>  nind <- 25
>  nnode <- 1
>  ncoef <- 1
>  k <- 2
> 
>  pred <- 0
>  fam <- 4
> 
>  theta <- 4 / 3
>  mu <- exp(theta)
>  x <- rpois(100, mu)
>  x <- x[x > k]
>  x <- x[1:nind]
> 
>  modmat <- matrix(1, nrow = nind, ncol = 1)
>  out <- mlogl(theta, pred, fam, x, modmat, modmat, deriv = 2,
+      type = "conditional")
> 
>  xxx <- seq(0, 100)
>  ppp <- dpois(xxx, mu)
>  ppp[xxx <= k] <- 0
>  ppp <- ppp / sum(ppp)
>  tau <- sum(xxx * ppp)
> 
>  all.equal(sum(x - tau), - out$gradient)
[1] TRUE
>  all.equal(length(x) * sum((xxx - tau)^2 * ppp), as.vector(out$hessian))
[1] TRUE
> 
>  foo <- function(theta) {
+      stopifnot(is.numeric(theta))
+      stopifnot(is.finite(theta))
+      stopifnot(length(theta) == 1)
+      mlogl(theta, pred, fam, x, modmat, modmat, type = "conditional")$value
+  }
> 
>  g <- grad(foo, theta)
>  all.equal(g, out$gradient)
[1] TRUE
> 
>  h <- hessian(foo, theta)
>  all.equal(h, out$hessian)
[1] TRUE
> 
>  foo <- new.env(parent = emptyenv())
>  bar <- suppressWarnings(try(load("ktp.rda", foo), silent = TRUE))
>  if (inherits(bar, "try-error")) {
+      save(list = c(paste("chisqout", 1:9, sep = ""), "out"), file = "ktp.rda")
+  } else {
+      print(all.equal(chisqout1, foo$chisqout1))
+      print(all.equal(chisqout2, foo$chisqout2))
+      print(all.equal(chisqout3, foo$chisqout3))
+      print(all.equal(chisqout4, foo$chisqout4))
+      print(all.equal(chisqout5, foo$chisqout5))
+      print(all.equal(chisqout6, foo$chisqout6))
+      print(all.equal(chisqout7, foo$chisqout7))
+      print(all.equal(chisqout8, foo$chisqout8))
+      print(all.equal(chisqout9, foo$chisqout9))
+      print(all.equal(out, foo$out))
+  }
[1] TRUE
[1] TRUE
[1] TRUE
[1] TRUE
[1] TRUE
[1] TRUE
[1] TRUE
[1] TRUE
[1] TRUE
[1] TRUE
> 
> 
> proc.time()
   user  system elapsed 
   0.25    0.04    0.28