Re: Expected value of the Geometric distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg118610] Re: Expected value of the Geometric distribution
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Wed, 4 May 2011 06:35:06 -0400 (EDT)
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 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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