Width vs. FWHM of LogNormal Distribution

[Andrea]

Hello everyone!

I'm fitting some data with a LogNormal distribution and saw that Fityk is giving me a parameter "width" and a parameter "FWHM". 

Can someone explain to me what the difference between the two is? 

Also I can find an uncertainty estimation for the width parameter under "Fit - Info" but I can't find it for FWHM. Do you know where to find the uncertainty estimate for FWHM?

Thanks in advance and all the best,

Andrea

[Marcin Wojdyr]

Hi Andrea,

I have a note in the source code that the FWHM is calculated using
eq. 28 of Maroncelli, M.; Fleming, G.R. J. Phys. Chem. 1987, 86, 6221-6239

The uncertainty of FWHM is not calculated.

Best wishes,
Marcin

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[Andrea]

I see, thank you so much!

[Dan Parshall]

I've had good results bootstrapping subsamples in order to measure uncertainty empirically.  Personally, I feel these are a better estimate of the uncertainty, since they answer the question "How similar would my results be, if I repeated the experiment?".

More formally, I believe that the standard uncertainties calculated just w.r.t. each variable are partial derivatives, considering the width of the function along each axis of the uncertainty function.  Whereas bootstrapping captures the full uncertainty, taking into account the correlations between the variables.  But it's been a while since I've looked at this, so take this with a grain of salt.  I think there's a good discussion in DS Sivia, "Data Analysis: a Bayesian Tutorial"

To view this discussion on the web visit https://groups.google.com/d/msgid/fityk-users/c29ce2fc-d802-4739-a88b-757f186691d9n%40googlegroups.com.

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Dan Parshall
Shorty George Productions
Washington, DC