R help - Mar 2006 - Estimation of skewness from quantiles of near-normal distribution

I have summary statistics from many sets (10,000's) of near-normal
continuous data.  From previously generated QQplots of these data I can visually
see that most of them are normal with a few which are not normal.  I have the
raw data for a few (700) of these sets.  I have applied several tests of
normality, skew, and kurtosis to these sets to see which test might yield a
parameter which identifies the sets which are visibly non-normal on the QQplot. 
My conclusions thus far has been that the skew is the best determinant of
non-normality for these particular data.

Given that I do not have ready access to the sets (10,000's) of data, only
to summary statistics which have been calculated on these sets, is there a
method by which I may estimate the skew given the following summary statistics:
0.1% 1% 5% 10% 25% 75% 90% 95% 99% 99.9% mean median N sigma

N is usually about 900, and so I would discount the 0.1%, 1%, 99%, and 99.9%
quantiles as unreliable due to noisiness in the distributions.

I know that for instance there are general rules for calculated sigma of a
normal distribution given quantiles, and so am wondering if there are any
general rules for calculating skew given a set of quantiles, mean, and sigma.  I
am currently thinking of trying polynomial fits on the QQplot using the raw data
I have and then empirically trying to derive a relationship between the
quantiles and the skew.

Thank you for any ideas.

Leif Kirschenbaum
Senior Yield Engineer
Reflectivity, Inc.
(408) 737-8100 x307
leif at reflectivity.com

This pertains to the first paragraph, you can use Dagostino test which is an
omnibus test combining both skewness and kurtosis and has a high power, istead
of only skewness of the data. Try ?dagoTest
   
  Ahmed

Leif Kirschenbaum <leif@reflectivity.com> wrote:
  I have summary statistics from many sets (10,000's) of near-normal
continuous data. From previously generated QQplots of these data I can visually
see that most of them are normal with a few which are not normal. I have the raw
data for a few (700) of these sets. I have applied several tests of normality,
skew, and kurtosis to these sets to see which test might yield a parameter which
identifies the sets which are visibly non-normal on the QQplot. My conclusions
thus far has been that the skew is the best determinant of non-normality for
these particular data.

Given that I do not have ready access to the sets (10,000's) of data, only
to summary statistics which have been calculated on these sets, is there a
method by which I may estimate the skew given the following summary statistics:
0.1% 1% 5% 10% 25% 75% 90% 95% 99% 99.9% mean median N sigma

N is usually about 900, and so I would discount the 0.1%, 1%, 99%, and 99.9%
quantiles as unreliable due to noisiness in the distributions.

I know that for instance there are general rules for calculated sigma of a
normal distribution given quantiles, and so am wondering if there are any
general rules for calculating skew given a set of quantiles, mean, and sigma. I
am currently thinking of trying polynomial fits on the QQplot using the raw data
I have and then empirically trying to derive a relationship between the
quantiles and the skew.

Thank you for any ideas.

Leif Kirschenbaum
Senior Yield Engineer
Reflectivity, Inc.
(408) 737-8100 x307
leif@reflectivity.com

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