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When only a certain range of the data is used for the fit, or when a range has been cut out, the PDFs need to be adjusted accordingly by removing the missing parts and renormalizing.
I'm thinking of something like this for the API
x = var('x', observed=True, vector=True)
mu = var('mu')
sigma = var('sigma')
model = Censor(x > 0, Normal(x, mu, sigma))