Re: Expected value of the Geometric distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg118618] Re: Expected value of the Geometric distribution
- From: Alexei Boulbitch <alexei.boulbitch at iee.lu>
- Date: Wed, 4 May 2011 19:46:52 -0400 (EDT)
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
--
Alexei Boulbitch, Dr. habil.
Senior Scientist
Material Development
IEE S.A.
ZAE Weiergewan
11, rue Edmond Reuter
L-5326 CONTERN
Luxembourg
Tel: +352 2454 2566
Fax: +352 2454 3566
Mobile: +49 (0) 151 52 40 66 44
e-mail: alexei.boulbitch at iee.lu
www.iee.lu
--
This e-mail may contain trade secrets or privileged, undisclosed or
otherwise confidential information. If you are not the intended
recipient and have received this e-mail in error, you are hereby
notified that any review, copying or distribution of it is strictly
prohibited. Please inform us immediately and destroy the original
transmittal from your system. Thank you for your co-operation.