I have a pulse profile (binned photon counts versus phase) of a star, and for each count rate I have its statistical error.

I want to calculate the so-called pulsed-fraction $P_{frac}=\frac{F_{max}-F_{min}}{F_{max}+F{min}}$, where $F_{max}$ and $F_{min}$ are the maximum and minimum count rates, respectively.

Is it possible to do propagation error to find the error for $P_{frac}$? If yes, how?

  • $\begingroup$ What kind of errors do your measurements have. I assume standard deviation. If not it might influence the method of error propagation. $\endgroup$
    – fibonatic
    Commented Mar 16, 2014 at 11:53
  • $\begingroup$ I am sorry, do you mean: what kind of distribution of the photon is assumed? If so, it is gaussian, yes. Otherwise please, could you explain me a little bit better what you mean? $\endgroup$
    – Py-ser
    Commented Mar 16, 2014 at 12:09

1 Answer 1


for simplicity of notation say $P = \frac{X - N}{X + N}$

given $\delta X$ is the uncertainty in X and $\delta N$ is the uncertainty in N


$\delta (X - N)$ = $\delta (X + N) = \sqrt {\delta ^2X + \delta ^2N}$

and therefore:

$\delta P = P \sqrt{(\frac{\sqrt {\delta ^2X + \delta ^2N}}{X - N})^2 + (\frac{\sqrt {\delta ^2X + \delta ^2N}}{X + N})^2}$

This is based upon equations 1b and 2b of the following reference:


  • $\begingroup$ And this is the $1\sigma$ confidence level, right? $\endgroup$
    – Py-ser
    Commented Mar 17, 2014 at 8:26
  • $\begingroup$ The propagation formula isn't limited to a particular number of standard deviations. If the uncertainity in Fmax and Fmin represent 1-sigma, then the unceratinty the formula gives will reflect 1-sigma. If the uncertainity is Fmax and Fmin represent 3-sigma, then the unceratinty the formula gives will reflect 3-sigma. You have to be consistent in the way you express the uncerainty for Fmax and Fmin; if you use n-sigma for Fmax, you have to use n-sigma for Fmin if you use the error propagation formula. $\endgroup$
    – DavePhD
    Commented Mar 17, 2014 at 14:08
  • $\begingroup$ thanks a lot! One last thing: can the statistical uncertainty I have on my data points be a standard deviation as well? I haven't understood the question of the user here. $\endgroup$
    – Py-ser
    Commented Mar 18, 2014 at 10:33
  • $\begingroup$ user fibonatic was asking, when you say "I have the statistical error", is this statistical error the standard deviation. The formula I gave you is based upon your error in Fmax and error in Fmin being a standard deviation or some particular multiple of the standard deviation, like 3 standard deviations. For example see equations 1b and 2b versus equations 1a and 2a in the referecnce I cited. $\endgroup$
    – DavePhD
    Commented Mar 18, 2014 at 11:49

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