🚀 go-pugleaf

Keywords: geometric standard deviation

I need to find a reference to verify the definition of the geometric
standard deviation.  Here is the particular problem:

Given a set of numbers x_1,...,x_n, let y_i = log x_i.
It can be shown that the geometric mean of the x_i is the same as
exp(ybar), where ybar is the arithmetic mean of the y_i.

I want to confirm that the geometric SD of the x_i is also
exp(ysigmahat), where ysigmahat is the standard deviation of the y_i.

I have a hunch that this is the way geometric SD is defined, but
I'd happily yield to corrections.  Moreover, if I am wrong, I'd
like to find a link between the GSD and exp(ysimgahat).

I am using this information to justify one way of estimating
the GM and GSD of a lognormal distribution without having to
explain MLE's and MME's.

Please reply by e-mail to this account; I'll summarize the responses
and re-post later.

Thanks.

Chad
s135@stat.Berkeley.EDU