`panel7pt1B.fn` <- function(){ # This function computes parameter estimates for the Impala data # under a distance sampling model that is reparameterized by # data augmentation having parameters "psi" and "sigma2" nz<-500 x<- sin( (impala[,5]/360)*(2*pi) ) *impala[,4] x<-x/100 nind<-length(x) y<-c(rep(1,nind),rep(0,nz)) x<-c(x,rep(NA,nz)) lik<-function(parms){ psi<-expit(parms[1]) sigma2<-exp(parms[2]) picap<-integrate( function(u){ exp(-(u^2)/sigma2)/4 },0,4)$value part1<- sum(log(psi*exp(-(x[1:nind]^2)/sigma2) ) ) part2<- nz*log( 1-psi*picap) -1*(part1+part2) } out<-nlm(lik,c(logit(175/(nz+nind)),log(1.2) ),hessian=TRUE) print(out) psihat<- expit(out$estimate[1]) N <-psihat*( nind+nz ) D<- N/48 cat("MLE Density: ",D,fill=TRUE) }