Suppose I have a black box that generates data following a normal distribution with mean m and standard deviation s. Suppose, however, that whenever it outputs a value < 0 it does not record anything (can’t even tell that it’s outputted such a value). We have a truncated gaussian distribution without a spike.
How can I estimate these parameters?
The model for your data would be:
Thus, the density function is:
ϕ(.) is the standard normal cdf.
You can then estimate the parameters μ and σ using either maximum likelihood or bayesian methods.