x<-rt(250,df=9)
par(pty="s")
qqnorm(x); qqline(x)
x<-rcauchy(250)
qqnorm(x)
qqline(x)
help(ppoints)
library(MASS)
help(fitdistr)
list(location=0,scale=1)
fitdistr(x,dcauchy,start=list(location=0,scale=1))
logLik(fitdistr(x,dcauchy,start=list(location=0,scale=1)))
logLik(fitdistr(x,dcauchy,start=list(location=0),scale=1))
help(optimize)
mu<-seq(from=-1,to=1,by=.1)
apply(outer(mu,x,logdcauchy),1,sum)
logdcauchy<-function(mu,x){
dcauchy(x,scale=1,location=mu,log=TRUE)}
apply(outer(mu,x,logdcauchy),1,sum)
loglikcauchy<-function(mu){
apply(outer(mu,x,logdcauchy),1,sum)}
logdcauchy
loglikcauchy
loglikcauchy(0)
optimize(loglikcauchy,lower=-1,upper=1)
result<-optimize(loglikcauchy,lower=-1,upper=1)
mu<-seq(from=-1,to=1,by=.01)
plot(mu,loglikcauchy(mu),type="l")
optimize(loglikcauchy,lower=-1,upper=1)
points(result[[1]],result[[2]])
negloglikcauchy<-function(mu){
-apply(outer(mu,x,logdcauchy),1,sum)}
optimize(negloglikcauchy,lower=-1,upper=1)
result<-optimize(negloglikcauchy,lower=-1,upper=1)
points(result[[1]],-result[[2]])
abline(h=-result[[2]]-(qchisq(0.95,1)/2))
mu<-seq(from=-.4,to=.4,by=.01)
optimize(negloglikcauchy,lower=-.4,upper=.4)
plot(mu,loglikcauchy(mu),type="l")
result<-optimize(negloglikcauchy,lower=-.4,upper=.4)
points(result[[1]],-result[[2]])
abline(h=-result[[2]]-(qchisq(0.95,1)/2))