Re: [Phys-L] Statistics question

[John Denker <jsd@av8n.com>]

On 08/24/2012 11:35 AM, Paul Nord wrote:
> Do you say "half-width" or Full Width at Half Max (FWHM)?  And what
> does it mean?

Well, the rule is simple:  Say what you mean, and mean what you say.

If you mean FWHM, say FWHM.  If you mean HWHM, say HWHM.

For typical well-behaved theoretical distributions, such as triangular,
rectangular, gaussian, et cetera, the maximum is well defined, and 
hence both the FWHM and HWHM are well defined.

 a) Note that the standard deviation is typically slightly smaller than
  the HWHM ... and therefore much closer to the HWHM than to the FWHM.

 b) Also, if you are using the "±" notation, it makes sense to talk 
  about ± HWHM  (not ± FWHM).

For these two reasons, I find myself talking about the HWHM more often
than the FWHM ...... but if you have a reason to talk about the FWHM
that's perfectly OK.  Say what you mean, and mean what you say.

For pictures and formulas pertaining to some familiar distributions, 
see
  http://www.av8n.com/physics/uncertainty.htm#sec-familiar-dist

========

For an empirical distribution, such as the histogram of arbitrary data,
you might find that the maximum, FWHM, and HWHM are not very well
behaved.  The mean and standard deviation are more likely to be well
behaved, but even that is not a sure thing.

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