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Re: CHISQR_CVF question. [message #67642 is a reply to message #67640]

Thu, 20 August 2009 01:03

Craig Markwardt
Messages: 1869
Registered: November 1996

Senior Member

On Aug 19, 4:42 pm, "R.G. Stockwell" <noemai...@please.com> wrote:
> "Paolo" <pgri...@gmail.com> wrote in message
>
> basically yes, abs(fft(ts))^2, and comparing it to chisquare from the
> IDL functions.
> I have worked on it, but I think the result is off by a factor of 2.
> That is a factor of 2 too stringent.
>
...
> Perhaps you can check my understanding. If we have a 95% significance
> level,
> then if we make a spectrum with 1000 points, shouldnt 50 of them be above
> that 95% line?

Let's say we have a time series, defined like this,
LC = time series values (array)
ERR = measurement uncertainty (array) of each LC point.

I define the power spectrum in the following way,
POW = ABS(FFT(LC,+1))^2 * ( 2 / TOTAL(ERR^2) )
which is to say, it is normalized by the total variance of the time
series, and a factor of 2. Assuming LC is real, then really only the
first half of POW is independent.

Then POW should be distributed like a chi-square with 2 degrees of
freedom. The mean value should be 2, the standard deviation should be
2. I just verified this with some random data.

I verified that CHISQR_CVF() produced reasonable numbers, compared to
my own MPCHILIM() function, which also computes confidence limits.
Sample code below.

Craig

lc = randomn(seed,2000)
err = dblarr(2000) + 1
POW = ABS(FFT(LC,+1))^2 * ( 2 / TOTAL(ERR^2) )
pow1 = pow(0:1000) ;; First half of power spectrum

print, avg(pow1)
;; ==> 1.9769791
print, stddev(pow1)
;; ==> 1.9997902

print, chisqr_cvf(0.05d, 2d)
;; ==> 5.9914659
print, mpchilim(0.05d, 2d, /slevel)
;; ==> 5.9914645
help, where(pow1 GE 5.9914645d)
;; ==> <Expression> LONG = Array[38]
;; (in other words, 38 out of 1000 or 3.8% of data exceeded
threshold)

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[Message index]

		Re: CHISQR_CVF question. By: David Fanning on Thu, 20 August 2009 09:57
		Re: CHISQR_CVF question. By: R.G. Stockwell on Thu, 20 August 2009 09:53
		Re: CHISQR_CVF question. By: Craig Markwardt on Thu, 20 August 2009 09:14
		Re: CHISQR_CVF question. By: R.G. Stockwell on Thu, 20 August 2009 08:21
		Re: CHISQR_CVF question. By: Craig Markwardt on Thu, 20 August 2009 01:03
		Re: CHISQR_CVF question. By: R.G. Stockwell on Wed, 19 August 2009 13:42
		Re: CHISQR_CVF question. By: pgrigis on Wed, 19 August 2009 12:29
		Re: CHISQR_CVF question. By: Craig Markwardt on Sat, 22 August 2009 10:51

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