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Math Help - Approximation of gaussian normalization factor

  1. #1
    Junior Member
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    Approximation of gaussian normalization factor

    hey,
    im working with a gaussian distribution
    P_\mu (x) = \frac{1}{A} e^{ - \frac{(x-\mu)^2}{2\sigma^2} }
    on a finite domain [a,b]. This of course means that the normalization factor A depends on \mu (as well as \sigma). I care less about accuracy and more about getting an analytic answer that does not involve integrals, and so looking for a way to approximate A. Namley, I'm looking for a function B_\mu such that:
    B_\mu \simeq \int_a^b e^{ - \frac{(x-\mu)^2}{2\sigma^2} } dx = A_\mu

    Any ideas?
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  2. #2
    MHF Contributor
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    Re: Approximation of gaussian normalization factor

    The normalisation facrtor can quickly be written in terms of the standard normal CDF. (im not sure, but from your post it looks like you might already have worked that out).

    Numerical approximations to the CDF are available, eg:
    Normal distribution - Wikipedia, the free encyclopedia
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