R version 2.12.1 (2010-12-16)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

  Natural language support but running in an English locale

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(bbmle)
Loading required package: stats4
Loading required package: numDeriv
Loading required package: lattice
> x <- 0:10
> y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
> d <- data.frame(x,y)
> fits <- lapply(c("optim","nlm","nlminb"),
+        mle2,
+        minuslogl=y~dpois(lambda=ymax/(1+x/xhalf)),
+        start=list(ymax=15,xhalf=6),data=d,
+        method="Nelder-Mead") ## 'method' is ignored by nlm()/nlminb()
Warning messages:
1: In dpois(x, lambda, log) : NaNs produced
2: In nlm(f = objectivefunction, p = start, hessian = !skip.hessian,  :
  NA/Inf replaced by maximum positive value
> sapply(fits,coef)
           [,1]      [,2]      [,3]
ymax  24.999725 24.999387 24.999424
xhalf  3.055245  3.055784  3.055781
> sapply(fits,logLik)
[1] -28.60406 -28.60405 -28.60405
> 
> (fit2 <-  mle2(y~dpois(lambda=25/(1+x/xhalf)),
+               start=list(xhalf=5),data=d,
+               lower=2,upper=8,
+               optimizer="optimize"))

Call:
mle2(minuslogl = y ~ dpois(lambda = 25/(1 + x/xhalf)), start = list(xhalf = 5), 
    optimizer = "optimize", data = d, lower = 2, upper = 8)

Coefficients:
   xhalf 
3.055659 

Log-likelihood: -28.6 
> 
> ## gives error referring to 'interval' rather than 'upper'/'lower'
> ## (fit2 <-  mle2(y~dpois(lambda=25/(1+x/xhalf)),
> ##              start=list(xhalf=5),
> ##              optimizer="optimize"))
> 
> proc.time()
   user  system elapsed 
  0.828   0.164   0.934