Formulas for Stable Calculation of Log Prob

[TheAeryan]

Hi,
For my current project I need a numerically-stable version of the truncated gaussian distribution in Python. I have been taking a look at the mathematical methods you detail in the file https://github.com/cossio/TruncatedNormal.jl/blob/23bfc7d0189ca6857e2e498006bbbed2a8b58be7/notes/normal.pdf for implementing the calculation of the mean and variance in a stable manner in Python.
Nonetheless, I also need a numerically stable method for calculating the log-probability of some value under the truncated gaussian (the f function you detail in the first paragraph of the PDF). Do you know how this can be done? I assume a similar method, based on Taylor expansions, could be used, but I'm not sure.

[cossio]

Hi, maybe something like this can work:

function tnlogpdf(x::Real, a::Real, b::Real)
    result = -x^2/2 - lognormcdf(a, b)
    if x < a || x > b
        return oftype(result, -Inf)
    else
        return result - log(two(result) * pi) / 2
    end
end