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Re: Expected value of the Geometric distribution

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  Re: Expected value of the Geometric distribution Bob Hanlon <hanlonr@cox.net> - 2011-05-04 10:35 +0000

#2089 — Re: Expected value of the Geometric distribution

dist = GumbelDistribution[a, b];

Moment[dist, 1]

a - b EulerGamma

Mean[dist]

a - b EulerGamma

ExpectedValue[x, dist, x]

a - b EulerGamma

Assuming[{Element[{a, b}, Reals], b > 0}, 
 Integrate[x*PDF[dist, x], {x, -Infinity, Infinity}]]

a - b EulerGamma


Bob Hanlon

---- 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
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