Data weighting on semi log scale

[raul_l]

Hi

I have to perform a fitting procedure on a semi logarithmic scale but I'm not sure how to weigh the experimental data points. I'm studying the decay of the luminescence of a certain type of crystals and the function I'm using has the form

$$I = \frac{1}{\tau} e^{-\frac{t}{\tau}} \frac{-Li_{2}(-erf(\sqrt{\frac{t}{\tau}})}{erf(\sqrt{\frac{t}{\tau}})}$$

where $$Li_{2}$$ and erf are the dilogarithm and error functions. (for simplicity I've omitted some constants). Basically, it's more or less a pure exponential with some nonlinearities at the beginning.

My adviser said that I should try to weigh each data point with the inverse of its value (or the square of inverse). Otherwise I get imprecise values for some of the parameters that depend on the smaller values of the data points. But I'm not sure if this is the right way to do this. It just doesn't feel right.

I was wondering if there are any general rules/guidelines for choosing the correct weights on a semi logarithmic scale.

 

[Redbelly98]

Your advisor is correct. Alternatively, you could take the log of the measured values and do a fit to them, with equal weighting.