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Re: Is " exp[ log-normal ] " a defined distribution ?
Posted:
May 18, 2006 11:26 AM
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Begin with a model of the form Y=a*X^b and transform it to Ln(Y) =
Ln(a) + b*Ln(X) and estimate Ln(a) and b via least squares regression.
Calculate a = Exp(Ln(a)). Then calculate predicted values of Y from Y
= a*X^b for the available data. The sum of the predicted values will
not be the same as the sum of the observed values... the residuals will
not sum to zero. Predictions from the completed model are biased. The
amount of that bias depends on several factors... the bias can be
trivial or it can be annoyingly large. If the data fit the model
"impressively" then the bias is probably not a big deal. Nonetheless,
there will be a bias. I find this to be of much more concern than the
distribution of the "errors". In some recent work with certain air
pollution data I've found the average bias to be in the range 20% - 40%
of the observed values, albeit this was very noisy data.
This "statistical bias" usually comes as a suprise to those who buy
exotic software and set themselves up as experts because they know how
to use SmartStat or whatever they bought.
This is another instance where a trip to Monte Carlo can be educational.
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