Re: Expected value of the Geometric distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg118596] Re: Expected value of the Geometric distribution
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Wed, 4 May 2011 06:32:35 -0400 (EDT)
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 at 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
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