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. Shant [[alternative HTML version deleted]]
On Sat, 29 Aug 2015, Shant Ch 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. >Sorry! My tired eyes missed the absolute value. FWIW, there are some quadrature packages on CRAN. Chuck
On 8/29/2015 4:00 PM, Charles C. Berry wrote:> On Sat, 29 Aug 2015, Shant Ch 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. >>Have you looked at "distr" and related packages on CRAN? Spencer Graves> > Sorry! My tired eyes missed the absolute value. > > FWIW, there are some quadrature packages on CRAN. > > Chuck > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >
Well, it's trivial to simulate, and for n=250000, for example, I get a mean of 6.875. Depending on your needs, you can choose a much larger sample to make it more precise, or, as Chuck suggested, try numerical integration. Cheers, Bert Bert Gunter "Data is not information. Information is not knowledge. And knowledge is certainly not wisdom." -- Clifford Stoll On Sat, Aug 29, 2015 at 2:00 PM, Charles C. Berry <ccberry at ucsd.edu> wrote:> On Sat, 29 Aug 2015, Shant Ch 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. >> > > Sorry! My tired eyes missed the absolute value. > > FWIW, there are some quadrature packages on CRAN. > > Chuck > > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.
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
X4 is being subtracted, not added.
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On August 29, 2015 5:24:55 PM PDT, 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?
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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