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Re: Expected value of the Geometric distribution

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Dear Tonja,
ConditionalExpression means that the expression is valid under a specified condition. Have a look at Menu/Help/ConditionalExpression.
In your case, in particular you can integrate with the needed condition from the very beginning. In this case it is called "Assumptions":

Integrate[
  E^(-E^(-((x - \[Mu])/\[Beta])) - (x - \[Mu])/\[Beta])/\[Beta]*
   x, {x, -\[Infinity], \[Infinity]},
  Assumptions ->  {\[Beta]>  0, \[Mu]>  0}]


EulerGamma \[Beta] + \[Mu]

Have fun, Alexei


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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Re: Expected value of the Geometric distribution Alexei Boulbitch <alexei.boulbitch@iee.lu> - 2011-05-04 23:46 +0000

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