Number 10 p24
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mle=2.55

> theta<-seq(1,4,.05)
> plot(theta,exp(20*(2.55-theta))*theta^(51),type='l')
> abline(h=.5)
> abline(h=.1)
> abline(h=.01)

Number 1 page 16
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like16<-function(theta,M=200,m=20,F=200,f=5){
# Give log likelihood for problem 1 page 16
l16<-(m+2*f)*log(theta)+(M-m)*log(1-theta)+(F-f)*log(1-theta^2)
l16}

> like16(.3)
[1] -99.84912
> like16(.1)
[1] -87.99219
> theta1_seq(.01,.3,.01)
> plot(theta1,like16(theta1),type='l')

max16<-function(theta.int,M=200,m=20,F=200,f=5){
qq<-nlminb(theta.int,neglike16,lower=0.01,upper=.99,M=M,m=m,F=F,f=f)
print(qq$messsage)
print(qq$grad.norm)
qq$parameter}

neglike16<-function(theta,M=200,m=20,F=200,f=5){
# Give log likelihood for problem 1 page 16
l16n<--((m+2*f)*log(theta)+(M-m)*log(1-theta)+(F-f)*log(1-theta^2))
l16n}

#--------------------------------------------------------------------------
# 2-d likelihood

extreme <- function(x){exp(x-exp(x))}

negextreme <- function(theta,data=x){
  # negative log likelihood for extreme value location/scale
  n <- length(data)
  mu <- theta[1]
  sig <- theta[2]
  nl <- n*log(sig)-sum((data-mu)/sig)+sum(exp((data-mu)/sig))
  nl}

maxextreme <- function(theta.int,data=x){
  # finds ml estimates of location/scale for extreme value data
  qq <- nlminb(theta.int,negextreme,lower=c(-Inf,0),data=data)
  qq$parameters}

plotextreme <- function(mu=seq(-.4,0,.01),sig=seq(.3,.8,.01),data=x){
  #does perspective plot of extreme likelihood surface
  n1 <- length(mu)
  n2 <- length(sig)
  parest <- maxextreme(c(mean(data),sd(data)))
  zmax <- -negextreme(parest,data=data)
  z <- matrix(0,n1,n2)
  for(i in 1:n1){for(j in 1:n2){
    z[i,j] <-  -negextreme(c(mu[i],sig[j]),data=data)-zmax}}
persp(mu,sig,z,xlab="mu",ylab="sigma",zlab="Rel.Like.")
list(mu=mu,sig=sig,z=z)}