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I need to bound a 1D gaussian/normal (or similar) probability density function in the domain interval $[-3\sigma, 3\sigma]$ in a way that still integrates to 1. I would need something like this:

$$ p(x) = \begin{cases} N(x;\mu, \sigma) &\text{if } -3\sigma \leq x \leq 3\sigma\\ 0 & \text{otherwise } \end{cases} $$

This is NOT a probability density function but how could I get a bounded distribution that is similar to the gaussian case?

Thanks in advance,

Federico

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    All you have to do is to divide $p(x)$ over by $\int_{-3 \sigma}^{3 \sigma} p(x) \mathrm{d} x$.2011-09-05
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    Agree with Shasha. Unless you want to demand that your function should vanish smoothly, then you'll need something else...2011-09-05
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    Thanks Sasha and valdo. What I actually need is that it vanished smoothly; I haven't commented on it in the question...2011-09-05
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    Do you know about [bump functions](http://en.wikipedia.org/wiki/Bump_function#Examples)?2011-09-05
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    If you just want something that looks similar, have you considered a scaled and centered beta distribution?2011-11-04

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