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Gaussian normal distribution curve

  1. Nov 9, 2004 #1
    I am looking for a mathematical equation which is similar to the Gaussian normal distribution curve, but I need one which terminates at a finite x = X and not at infinity, ie, [tex]f(x \geq X) = 0[/tex], but, [tex] f(x \leq X) = [/tex]a function which has a Gaussian shape-like curve.
    Is there one such as this that you know or in mathematics literatures?
  2. jcsd
  3. Nov 9, 2004 #2
    define the Gaussian for any finite interval
    = gaussian for a<x<b
    = 0 otherwise

    -- AI
  4. Nov 9, 2004 #3


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    Or consider:
    for [itex]|x|<\sqrt{\ln(A/b)}[/itex] and 0 elswhere.
    That one is even continuous.
  5. Nov 9, 2004 #4


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    Or even just a raised cosine, 1 + cos(x) : -pi < x < pi .
  6. Nov 9, 2004 #5
    Is there a mathematical function which is not piece-wise and can be defined for the whole range of x (just by one mathematical relationship)?
  7. Nov 9, 2004 #6

    matt grime

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    Probably not since you are splitting the range up in your own requirements, besides, that is purely a superficial issue for you. If you know what a heaviside function is then, for k some positive real number


    for some suitably shaped and nomalized function would do and would appear to be a nice single line wouldn't it? Of course

    H(y) is defined piecewise.
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