## GEOSTATS: Back transforming log-normal data

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• I would have to dissagree with Pierre s difinitive You can t . If we make a probability statement such as Prob(ll
Message 1 of 1 , May 11, 1998
I would have to dissagree with Pierre's difinitive "You can't". If we make
a probability statement such as Prob(ll < mu < ul) = 90%, (ie construct a
confidence interval for the block mean of log transformed data) , then we
are able to also make the probability statement Prob(f(ll) < f(mu) < f(ul))
= 90% provided that the function f is a one to one function. In the case of
log transformed data, the function we want here is the exponential and as
Pierre notes we may corect for bias using s^2/2 or this can be refined
slightly as mentioned by Cressie 1990 where the bias correction is
porportional to s^2/2. If we do not correct for bias (ie use just the
exponential function, then we have a confidence interval for the median
exp(mu) of the lognormal distribution.

In general the idea of back transforming the confdence limits is a fairly
standard technique throughout the statistical literature.
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