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?

**Answer**

The model for your data would be:

yi∼N(μ,σ2)I(yi>0)

Thus, the density function is:

f(yi|−)=exp(−(yi−μ)22σ2)√2πσ (1−ϕ(−μσ))

where,

ϕ(.) is the standard normal cdf.

You can then estimate the parameters μ and σ using either maximum likelihood or bayesian methods.

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