We show using Monte Carlo methods that serious systematic error may be introduced in the nonlinear least‐squares (NLLSQ) fitting of Lorentzian line spectra of poor statistical quality or with too few data points in the lines. For such spectra we have found that the NLLSQ estimates of Lorentzian linewidth error are unreliable. This has the result of causing the weighted mean linewidth from several similar spectra to be unequal to the result obtained by adding the spectra together channel by channel and then doing the NLLSQ fit. The problem is illustrated using examples from Mössbauer spectroscopy, however, the results appear to be quite generally relevant in all cases where statistically marginal data are fit with Lorentzian lines.

Topics
Mossbauer spectroscopy, Regression analysis, Monte Carlo methods
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© 1974 The American Institute of Physics.
1974
The American Institute of Physics
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