I have $n$ samples which follow a logistic distribution with unknown $u$ and $s$; it is affected by a Gaussian noise with 0 mean. I would like to estimate its average $u$ with a confidence interval (let's say 95%).
I did computed the data set average $x$, and the data-set variance $v$. As Wikipedia says, I should do this... I am confused on how to get the correct parameters in $t$, if $t$ is a t-student distribution.
I found a shady example which is supposed to have a 95% confidence interval
x <- c(0.39, 0.68, 0.82, 1.35, 1.38, 1.62, 1.70, 1.71, 1.85, 2.14, 2.89, 3.69)
s2 <- var(x)
mx <- mean(x)
n <- length(x)
a <- qt(0.975, df = n - 1) * sqrt(s2 / n)
l.inf <- mx – a
l.sup <- mx + a
cat("(",l.inf,":",l.sup,")\n")
qt generates a t-student distribution in R
Will it work on my data? Should I calculate the Phi over the Gaussian tables? because I do not recognize that shady 0.975 (95%) or 0.995 (99%) of the example, is it $1-((1-0.99)/2)$ ?
