Re: Symmetry and moments counterexample

In article <1138670641.950869.75380@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Reef Fish <Large_Nassau_Grouper@xxxxxxxxx> wrote:

>Herman Rubin wrote:

>> >If F and G have all the moments equal they "usually" the same
>> >distribution.

>Here's a sidebar question to that statement.

>If none of the n>0 moments exist for two distributions, would one say
>they have "all the moments equal" where "equality" might mean
>undefined or infinity?

>If so, there would be members of different disbritions in the stable
>family of distribution for which no moments exists, such as Levy's
>distribution.

>-- Bob.

I do not think that this was what was in mind. It is, of
course, an answer to the precise question. However, it is
somewhat of a surprise that distributions with all moments
exist, but which are not determined by their moments.
Stieltjes appears to be the first who exhibited such examples.

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

Relevant Pages