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Math Help - What distribution is this?

  1. #1
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    What distribution is this?

    Let s(x)=exp(-(\frac{x}{2})^c)

    x\ge 0, c>0

    How does the distribution look like? Can I conclude that s(x) takes the form of an exponential distribution?
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  2. #2
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    yeh...

    Quote Originally Posted by noob mathematician View Post
    Let s(x)=exp(-(\frac{x}{2})^c)

    x\ge 0, c>0

    How does the distribution look like? Can I conclude that s(x) takes the form of an exponential distribution?
    yes this takes form of exponential distribution.
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    Quote Originally Posted by noob mathematician View Post
    Let s(x)=exp(-(\frac{x}{2})^c)

    x\ge 0, c>0

    How does the distribution look like? Can I conclude that s(x) takes the form of an exponential distribution?
    Since there is no normalising constant (which will be \frac{1}{\Gamma \left(\frac{c+1}{c}\right)}, by the way) it does not define a pdf. Overlooking that, I don't think it has any special name. It certainly is NOT an exponential distribution. The closest I can think of is the exponential power distribution (except it's not).
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    O sorry but, y can't it be exponential ?
    I thought it is exponential because, as C is a constant, its value can b found by integrating the fn' . Isn't this interpertation correct.
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    Quote Originally Posted by amul28 View Post
    O sorry but, y can't it be exponential ?
    I thought it is exponential because, as C is a constant, its value can b found by integrating the fn' . Isn't this interpertation correct.
    IF c = 1 then the function, after being multiplied by an appropriate normalising constant, will define an exponential pdf.
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    Actually was asking about how it will look like.. But i guess exponential will be the closer and given that x is only defined >0
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    Quote Originally Posted by noob mathematician View Post
    Actually was asking about how it will look like.. But i guess exponential will be the closer and given that x is only defined >0
    Try different values of c eg. c = 1/2, 1, 2, 3. Plot the graphs. What do you find?

    c = 1/2: plot y = Exp[-(x/2)^1/2] - Wolfram|Alpha

    c = 1: plot y = Exp[-(x/2)^1] - Wolfram|Alpha

    c = 2: plot y = Exp[-(x/2)^2] - Wolfram|Alpha

    c = 3: plot y = Exp[-(x/2)^3] - Wolfram|Alpha
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