In article <[EMAIL PROTECTED]>,
Glen Barnett <[EMAIL PROTECTED]> wrote:
>Dennis Roberts wrote:
>> unless you had a table comparable to the z table for area under the normal
>> distribution ... for EACH different level of skewness ... an exact answer
>> is not possible in a way that would be explainable
>Even if you specify level of skewness, an exact answer is still not
>possible without specifying more about the distribution. Specifying to
>third moments (for example) doesn't pin disributions down very well at
>all.
Even if the moments of the distribution are exactly those
of the normal distribution, you need lots of moments to
guarantee that the distribution is close to normal.
If the first 20 moments are exactly those of the standard
normal, one can conclude that the cdf at 0 is between
0.3 and 0.7, but not that it is between 1/3 and 2/3. To
improve this by a factor of 10, the number of moments
needed is in the thousands.
--
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, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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