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Math Help - Looking for a PDF

  1. #1
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    Looking for a PDF

    Hello,

    Does anyone know a probability distribution with the following characteristics:
    Univariate
    With only one parameter
    Supported over the real line (-8,+8)
    The expected value can be any real number
    ...?

    For example, the Exponential distribution has all these characteristics but the support over the real line...

    Thx a lot
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  2. #2
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    Quote Originally Posted by lalohurtado View Post
    Hello,

    Does anyone know a probability distribution with the following characteristics:
    Univariate
    With only one parameter
    Supported over the real line (-8,+8)
    The expected value can be any real number
    ...?

    For example, the Exponential distribution has all these characteristics but the support over the real line...

    Thx a lot
    I don't see how the expected value can be any real number if the support is a bounded interval .....
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  3. #3
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    Correction

    The support is not bounded... I screwed up by writing "eights" instead of "Infinity" signs...

    Answer? Anyone?...
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  4. #4
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    Quote Originally Posted by lalohurtado View Post
    The support is not bounded... I screwed up by writing "eights" instead of "Infinity" signs...

    Answer? Anyone?...
    No use being impatient when the delay is your own making.

    A pdf that satisfies your criteria (the Logistic distribution) can be found here: Logistic distribution - Wikipedia, the free encyclopedia
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  5. #5
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    Almost, but not quite...

    The logistic distribution has two parameters... one for location and another for scale.

    Thanks for the reply though...
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  6. #6
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    t-distribution.

    Or you can construct one. For instance, if X is exponential, then log X is a one-parameter infinite support random variable.
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  7. #7
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    Txs a lot...

    but I'd appreciate some more help...

    The t distribution would not work for me because the one-parameter version is centered at 0, and cannot take any real value as Expected value...

    I had thought of the log-exponential distribution. But the thing with it is that its expected value is ridiculously difficult to express... and untractable for all practical purposes...

    You are right, the log-exponential fits my requirements... but I want to ask for help again to find another distribution that fits my requirements, but with a tractable expression for the expected value.

    Sorry for being a pain! but I'll appreciate any help!
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  8. #8
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    Take any two-parameter distribution with infinite support, fix one of the parameters to a constant and voila, you have a one-parameter distribution satisfying your requirement.

    Seriously though, what's the point of finding such a distribution?
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