Groups > comp.soft-sys.math.mathematica > #2068

Expected value of the Geometric distribution

From	"Tonja Krueger" <tonja.krueger@web.de>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Expected value of the Geometric distribution
Date	2011-05-03 12:22 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<ipos29$i2t$1@smc.vnet.net> (permalink)

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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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Expected value of the Geometric distribution "Tonja Krueger" <tonja.krueger@web.de> - 2011-05-03 12:22 +0000
  Re: Expected value of the Geometric distribution Peter Breitfeld <phbrf@t-online.de> - 2011-05-04 23:48 +0000

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