R Under development (unstable) (2023-12-07 r85661 ucrt) -- "Unsuffered Consequences"
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> library(bbmle)
Loading required package: stats4
> old_opts <- options(digits=3)
> x <- 0:10
> y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
> d <- data.frame(x,y)
> suppressWarnings(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()
> 
> sapply(fits,coef)
       [,1]  [,2]  [,3]
ymax  25.00 25.00 25.00
xhalf  3.06  3.06  3.06
> sapply(fits,logLik)
[1] -28.6 -28.6 -28.6
> 
> (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 
 3.06 

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"))
> options(old_opts)
> 
> proc.time()
   user  system elapsed 
   1.14    0.18    1.31