Jerry Dallal wrote:
>
> While not disagreeing with anything that Professor Rubin has said, I'd
> add that it depends on what you want or need. For example, if you
> want the value for a specific problem rather than a general formula,
> simulation will often be able to get it for you.
I have purchase data from a marketing study. By looking at the
spread of amounts for a given customer, we hope to determine if a
particular customer is more likely to 1) buy our full range of
products, 2) buy only our lower priced products, or 3) buy only our
higher priced products.
If you histogram the purchase amount data, ignoring who bought what,
the data fits a gamma-distribution pretty well. We believe that it is
reasonable to assume that, within a single account, a standard deviation
of amounts consistent with the overall gamma distribution indicates
someone utilizing the full product line, whereas a standard deviation
much smaller than expected indicates someone interested in products from
a specific price range. As always, it is important to figure out how
much "smaller than expected" is statistically significant, given a
particular sample size.
Given that background, here is my concern about your suggestion.
The parameters of the gamma-distribution have been empirically fit.
There is no particular justification for this, except that the amount
data is obviously skewed, and the gamma distribution is flexible enough
to fit a number of different data "shapes". I am wary, however, of
doing a numerical simulation based on an empirical fit, feeling that
applying numerics to empirics takes me too far away from my original
data. Am I being too conservative here?
(Also, I am just plain curious as to whether determining the
standard deviation of a sample standard deviation is a problem that has
already been solved, proven unsolvable, or somewhere in between.)
-- Andrew
.
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