[R] Fw: Multiple Integrals

[Shant Ch]

Thank you very much to all for all your responses.

@Dr. Winsemius, E[f(X)] >=f(E(X)) if f is convex. Now we know |x| is convex function, so clearly in this scenario if we compute the expectation of the ((X1+X2+X3)/3-X4) and then take the absolute, then, we will get a lower bound of the expectation I want to find. 

      On Saturday, August 29, 2015 7:24 PM, David Winsemius <dwinsemius at comcast.net> wrote:
   

 
On Aug 29, 2015, at 11:35 AM, Shant Ch via R-help wrote:

> Hello Dr. Berry,
> 
> I know the theoretical side but note we are not talking about expectation of sums rather expectation of ABSOLUTE value of the function (X1/3+X2/3+X3/3-X4), i.e. E|X1/3+X2/3+X3/3-X4|  , I don't think this can be handled for log normal distribution by integrals by hand.
> 

To Shnant Ch;

I admit to puzzlement (being a humble country doctor). Can you explain why there should be a difference between the absolute value of an expectation for a sum of values from a function, in this case dlnorm,  that is positive definite versus an expectation simply of the sum of such values?

-- 

David Winsemius
Alameda, CA, USA


   
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