On Aug 30, 2015, at 8:41 AM, Shant Ch via R-help wrote:
> 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
> <dwinsem...@comcast.net> wrote:
Using the adaptIntegrate function in package:cubature I seem to be getting
convergence near 5.359359 as I extend the limits of integration. I don't think
that `adaptIntegrate` can handle infinite range. Either than or the NaN it is
returning is a signal of pathology that I don't understand.
> require(cubature)
> fx<-function(x){
+ dlnorm(x,meanlog=2.185,sdlog=0.562)
+ }
> I.4d <- function(x) {
+ x1 = x[1]; y1 <- x[3]
+ x2 = x[2]; y2 <- x[4]; abs(y1/3+y2/3+x1/3-x2)*fx(y1)*fx(y2)*fx(x1)*fx(x2)}
>
> adaptIntegrate(I.4d, rep(0, 4), rep(1000, 4), maxEval=1000000)
$integral
[1] 5.359082
$error
[1] 0.001922979
$functionEvaluations
[1] 1000065
$returnCode
[1] 0
> I.4d <- function(x) {
+ x1 = x[1]; y1 <- x[3]
+ x2 = x[2]; y2 <- x[4]; abs(y1/3+y2/3+x1/3-x2)*fx(y1)*fx(y2)*fx(x1)*fx(x2)}
>
> adaptIntegrate(I.4d, rep(0, 4), rep(100, 4), maxEval=1000000)
$integral
[1] 5.357679
$error
[1] 0.001820893
$functionEvaluations
[1] 1000065
$returnCode
[1] 0
> I.4d <- function(x) {
+ x1 = x[1]; y1 <- x[3]
+ x2 = x[2]; y2 <- x[4]; abs(y1/3+y2/3+x1/3-x2)*fx(y1)*fx(y2)*fx(x1)*fx(x2)}
>
> adaptIntegrate(I.4d, rep(0, 4), rep(10000, 4), maxEval=1000000)
$integral
[1] 5.359359
$error
[1] 0.001871926
$functionEvaluations
[1] 1000065
$returnCode
[1] 0
Best;
David.
>
>
>
> 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
>
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
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David Winsemius
Alameda, CA, USA
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