I have sampled a number of $x$ values from a normal distribution with mean 0 and sd 0.2. I then transformed these $x$ values to $y$ values using the formula $y = e^x/(e^x + 1)$. I know that the $y$ values will have a mean of 0.5 and all lie between 0 and 1.
- Do these y values fit some common distribution?
- Is there a way to figure this out in R?
What I am looking for is if there is a simple distribution to describe the y values that would allow me to describe it in terms of a few parameters and possibly sample directly from it in R.