[fitsbits] ATNF/NRAO codes for polarization

[Peter Teuben]

Tom,
   

  we'll probably need some proper definitions, at least for kurtosis, i
can see two variations.
Here's what I normally use

mean=sum1/sum0                                       is probably not so
controversial
variance = sum2/sum0 - mean*mean         probably also ok, some people
might use the N-1

I happen to prefer a kurtosis that gives 0 for a gauss, but then I use it as


           ((sum4-4*sum3*mean+6*sum2*mean*mean)/sum0 -
3*mean*mean*mean*mean) /
           (variance*variance) -3.0;


and a skewness as

((sum3-3*sum2*mean)/sum0 + 2*mean*mean*mean) / (sigma*sigma*sigma);

with sigma = sqrt(variance)

is again probably less controversial.


(of course these code snippets can be dangerous if you don't de-bias
your numbers
to the mean before taking such higher order moments)


In some fields (see e.g. van der Marel & Franx (1993))  h3 and h4 are
the common
3rd and 4th order moments,
    h3 = skewness / 4 sqrt(3)
    h4 = kurtosis / 8 sqrt(6)

in your writeup it will be useful to add this, and perhaps more, examples.

I'm a little opaque on your meaning for 15,17,19   and 16,18. I've never
seen
those used. Are those even higher moments?

 - peter

On 12/16/2012 04:56 PM, Tom Kuiper wrote:
> I would like to extend these codes as follows to handle signal statistics:
>
>   Number Code      Meaning
> 11     mean (should be zero for Gaussian noise)
> 12     variance (proportional to power)
> 13     skewness (should be zero for Gaussian noise)
> 14     kurtosis (should be 3 for Gaussian noise)
> 1x     x = 5,7,9 (should be zero for Gaussian noise)
> 1y     y = 6,8 (should be 15, 105 for Gaussian noise)
>
> Does anyone anticipate a problem with that?  Of course, some analysis 
> software might choke on this instead of gracefully ignoring unknown codes.
>
> Best regards
>
> Tom
>
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