[Ifeffit] third cumulant and radial distribution function

[Matt Newville]

Hi Chiara,

On Sat, Jul 12, 2008 at 2:58 PM, chiara maurizio <maurizio at esrf.fr> wrote:
> matt,
>
> I have a problem with an exafs analysis:
> from the exafs analysis (with feffit2.98) of the first shell of a disordered
> system
> I get the first three cumulants.
> now, I wander how can reconstruct from them the radial distribution function
> which is the best solution? I have tried with the skew-normal distribution,
> but for the high skewness (ratio of third cumulant to sigma3)
> values I get - that is around 2.5 - it is not well defined.
> Do you have a suggestion?
> Thanks,

Hmm, you mean you get a number for "third" that is 2.5 times the
number for "sigma2"?  That seems huge.
I think that may mean that the pair distribution function is so skewed
that the cumulant expansion out to third order may not be complete
enough to be useful (some say at this point that the cumulant
expansion "breaks down", but as it is a simple measure of the moments
of a distribution, it seems to me that it is always valid, but not
necessarily useful).

When the higher order cumulants become large, a histogram approach
might be more meaningful.  To do this, you can  make a series of paths
at 0.1Ang spacing (as an example), around your expected bond length,
assign each of them a sigma2 value (perhaps a variable that is
constrained for all paths to be the same) and a relative amplitude for
each path that follows some arbitrary distribution function.    Then
you can have the fitting adjust the amplitude parameters for the
distribution function.   In this way, nearly arbitrary distribution
functions can be modeled, though with some effort.

Is that a reasonable approach for your situation?  If not,  can you
give some more details for this system?

--Matt