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Re: Expected value of the Geometric distribution

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  Re: Expected value of the Geometric distribution DrMajorBob <btreat1@austin.rr.com> - 2011-05-04 10:32 +0000

#2076 — Re: Expected value of the Geometric distribution

You need Assumptions:

Integrate[
  x PDF[GumbelDistribution[\[Alpha], \[Beta]],
    x], {x, -\[Infinity], \[Infinity]},
  Assumptions -> {Element[\[Alpha], Reals], \[Beta] > 0}]

\[Alpha] - EulerGamma \[Beta]

Bobby

On Tue, 03 May 2011 07:22:14 -0500, Tonja Krueger <tonja.krueger@web.de>  
wrote:

> Dear everybody,
> Thank you all for your kind help. But I'm still stuck trying to find the  
> expected value for a continuous distribution like the Gumbel  
> distribution or GEV, Weibull.
> Moment[GumbelDistribution[\[Alpha], \[Beta]], 1]
> gives this as result:
> \[Alpha] - EulerGamma \[Beta]
> But when I try using
> Integrate[ E^(-E^(-((x - \[Mu])/\[Beta])) - (x -  
> \[Mu])/\[Beta])/\[Beta]* x, {x, -\[Infinity], \[Infinity]}]
> This is what I get:
> ConditionalExpression[\[Beta] (EulerGamma + Log[E^(\[Mu]/\[Beta])] -  
> E^-E^((\[Mu]/\[Beta])) Log[E^(-(\[Mu]/\[Beta]))] +  
> Log[E^(\[Mu]/\[Beta])])), Re[\[Beta]] > 0]
> I am stumped.
> Tonja
> ___________________________________________________________
> Schon geh=C3=B6rt? WEB.DE hat einen genialen Phishing-Filter in die
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>


-- 
DrMajorBob@yahoo.com

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