# Computation of parameters of truncated normal distribution

I have a numeric data sample with mean $\mu$ and standard deviation $\sigma$. I believe that this data has a normal distribution truncated to $[0,1]$.

1. Is there a reasonably simple formula for estimating the parameters $\mu', \sigma'$ of that truncated normal distribution? Is there an R command which does it?

2. I understand that I could find $\mu', \sigma'$ by applying a maximum-likelihood fitting algorithm directly to my data (through, say, fitdistr in R).

3. Is there some good understanding how much more precise approach (2) is over approach (1)? Say the sample size is from 10 to 100, $\mu=0.75,$ $\sigma=0.15$.

• Out of curiosity--because this is a pretty unusual thing to encounter--what application is it that models data in $[0,1]$ using truncated normal distributions?
– whuber
Commented Jun 27, 2014 at 19:07
• @whuber: I chose truncated normal distribution to model student percentile scores. I made this decision based on available data to me. There is no strong theoretical reason to choose it, but (as far as I know) neither there is one for other distributions.