>At 08:56 PM 10/20/99 -0400, you wrote:
>... snip ...
>>I believe the first thing to do in finding an exponential curve fit is to
>>take the log of the data, then apply a linear fit. (?) That is how I would
>>do it anyway. This would produce identical results to the accuracy of the
>>logarithm.
>>
>>-Lucas
This is **not** the correct way to fit an exponential when you have "real"
(i.e., experimental) data. The reason is that for least-squares fitting to
be a maximum likelihood estimator of the "true" function, the measurement
errors for each data point must be independent and normally distributed
with constant standard deviation. Thus, if your data confrom to these
requirements, doing a non-linear transformation (such as taking the log)
will result in "data" that do not conform to these requirements. In
practical terms, there is usually little difference between a nonlinear fit
to exponential data and a linear fit to the same logarithmically
transformed data, but sometimes there is a difference, so to be sure, one
should never transform the data before fitting.
How this applies to "fitting" Mersenne numbers is not clear, since the
concept of measurement errors, or uncertainty, doesn't really apply, as
best I can see. A maximum entropy method might be just as good as a
least-squares approach. (Of course, another fundamental underlying
assumption of any fitting procedure is that you are using the correct, or
"true", functional form, which is not known in this case, or perhaps
doesn't even exist!)
Tony Pryse
*****************************************************
* Kenneth M. (Tony) Pryse
* Department of Biochemistry and Molecular Biophysics
* Washington University School of Medicine
* St. Louis, MO 63110
* [EMAIL PROTECTED]
* 314-362-3345
*****************************************************
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