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Math Help - I need the function for a Gauss curve

  1. #1
    polecat1
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    I need the function for a Gauss curve

    Hello,

    I am doing a fuzzy logic simulation and I need a function that will generate values for me. These values need to approximate a Gauss (Bell, Normal) Curve for a particular range. I need it to generate the y value for a given x. The left side will of course be located at (0,0), the top should be (6,1) and the rightmost side should be (12,0). I can't for the life of me remember how to do something like this and I need this fuction for this project due this weekend.

    Thanks a ton for any help.

    Polecat
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by polecat1 View Post
    Hello,

    I am doing a fuzzy logic simulation and I need a function that will generate values for me. These values need to approximate a Gauss (Bell, Normal) Curve for a particular range. I need it to generate the y value for a given x. The left side will of course be located at (0,0), the top should be (6,1) and the rightmost side should be (12,0). I can't for the life of me remember how to do something like this and I need this fuction for this project due this weekend.

    Thanks a ton for any help.

    Polecat
    As Gaussian (Bell) curve centered at 0 has the equation:
    y = e^{-x^2}
    and stretches to \pm \infty on each side. You can't terminate it on one end or the other.

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    As Gaussian (Bell) curve centered at 0 has the equation:
    y = e^{-x^2}
    and stretches to \pm \infty on each side. You can't terminate it on one end or the other.

    -Dan
    Are you sure?

    I think it should be,
    \frac{1}{\sqrt{2\pi}} e^{-x^2/2}

    Because in the way you said it, it is not a probability density function since \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}.
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    Are you sure?

    I think it should be,
    \frac{1}{\sqrt{2\pi}} e^{-x^2/2}

    Because in the way you said it, it is not a probability density function since \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}.
    (chuckles) Okay! Okay! What he said.

    -Dan
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by polecat1 View Post
    Hello,

    I am doing a fuzzy logic simulation and I need a function that will generate values for me. These values need to approximate a Gauss (Bell, Normal) Curve for a particular range. I need it to generate the y value for a given x. The left side will of course be located at (0,0), the top should be (6,1) and the rightmost side should be (12,0). I can't for the life of me remember how to do something like this and I need this fuction for this project due this weekend.

    Thanks a ton for any help.

    Polecat
    Do you want a normal random number generator?

    RonL
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  6. #6
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    Quote Originally Posted by polecat1 View Post
    I am doing a fuzzy logic simulation and I need a function that will generate values for me. These values need to approximate a Gauss (Bell, Normal) Curve for a particular range. I need it to generate the y value for a given x. The left side will of course be located at (0,0), the top should be (6,1) and the rightmost side should be (12,0).
    There are several "bell shaped" curves with finite support commonly used to define fuzzy membership functions, which are not Gaussian (which has infinite support), such as the generalize bell curve and the pi curve. See, for instance:

    Generalized Bell Curve

    Pi Curve


    -Will Dwinnell
    Data Mining in MATLAB
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