`panel5pt4.fn` <-
function(){
## double observer model for estimating population size for the
## aerial waterfowl survey data described in Section 5.5.3


y<-c(64,19,79)
# order of counts is: (seen by both, seen by 2nd only, seen by 1st only)
nind<-sum(y)

lik<-function(parms){
p<-  expit(parms[1:2])
n0<- exp(parms[3])
N<-nind + n0
pvec<-c(p[1]*p[2],(1-p[1])*p[2],p[1]*(1-p[2]),(1-p[1])*(1-p[2]))
-1*(lgamma(N+1)-lgamma(n0+1) +  sum(c(y,n0)*log(pvec)))
}


 nlm(lik,c(0,0,1),hessian=TRUE)



}