In the following program I can't find the right way to get the answer. I mean, can't find the right parameter value:
f.sigma <- function(sigma, x)
{
n <- length(x)
sum1 <- sum(x^2)
sum2 <- sum(log(1-exp(-1*(x/sigma)^2)))
sum3 <- sum(x^2/(exp((x/sigma)^2)-1))
ans <- -1*n + sum1/sigma^2 + (n/sum2+1)/sigma^2*sum3
return(ans)
}
burrx.mle1 <- function(x, lower, upper)
{
n <- length(x)
sigma.root <- uniroot(f.sigma, interval=c(lower,upper), x=x)
sigmahat <- **sigma.root$root**
thetahat <- -1*n/sum(log(1-exp(-1*(x/sigmahat)^2)))
ans <- list(theta.hat=thetahat, sigma.hat=sigmahat)
return(ans)
}
burrx.mle1(c(4,1,5),1,5)
another thing what does it mean my sigma.root$root? basically what is the use of $root? here in burrx.mle1(c(4,1,5),1,5) what does it mean my c(4,1,5)?