[R] hypergeometric & population estimates

[Jesse.Whittington@pc.gc.ca]

"help"

We want to estimate the number of caribou in Jasper.  We recently conducted
an aerial survey and saw 70 uncollared caribou and 8 of 11 collared
caribou.  We want to estimate the number of caribou in this population with
95% confidence limits.  Gary White uses the hypergeometric distribution and
determines the population estimates using maximum likelihood and 95%CL as
-2LogLikelihoods.  Below, I determined the population estimate using
dhyper(x,m,n,k) and maximizing the density value as a function of n, but do
not know how I should calculate MLE with this distribution.


x <- 8         # number resighted caribou (white balls drawn)
m <-11         # number collared caribou (white balls total)
k <- 70        #  number caribou seen (# balls drawn)
n <- 1:500     #  ?? unknown number of uncollared caribou (# black balls)

d <- unlist(lapply(n, function(i) dhyper(x,m,i,k)))     # density estimate
for each value of n
data <- data.frame(estimate = n+m, d)
data <- data[is.finite(data$d), ]             # filter out NA's

max.d <- max(data$d)
pop.estimate <- data[data$d == max.d, 1]

Thank-you for your assistance,
Jesse