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Math Help - "Continuous" binomial distribution

  1. #1
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    "Continuous" binomial distribution

    Hi.

    I want to use some kind of "continuous" binomial distribution. I know binomial distribution is defined for natural numbers, but I want to extend it to the use of real numbers.

    I also know that the gamma function is an extension of factorial to be used with real numbers.

    My question is:

    Is f(x) = \frac{\Gamma(n+1)}{\Gamma(x+1)*\Gamma(n+1-x)} p^x (1-p)^{n-x} a probability density function? More precisely, is the integral from 0 to n equal to 1?

    Playing with excel it doesn't seem to be 1, but i'm not sure. Do you know what function should i use?

    Thanks.
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  2. #2
    MHF Contributor matheagle's Avatar
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    You may want to look at a Beta random variable.
    http://en.wikipedia.org/wiki/Beta_distribution
    If you want to extend it's support from (0,1) to say (0,n) you can tranform it by letting W=nX.
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  3. #3
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    Thanks! That's what I was looking for!
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  4. #4
    MHF Contributor matheagle's Avatar
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    The Beta is a generalization of a U(0,1) rv.
    If you let \alpha=\beta=1 you get a U(0,1).
    Do you know how to transform a rv, so the support is (0,n) instead?
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