The dispersion (standard deviation) of the estimator of neutron flux number

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Discussion Overview

The discussion revolves around estimating the neutron flux from a source using a detector that counts neutrons over a one-minute interval. Participants explore the statistical properties of the maximum likelihood estimator for the neutron flux and its dispersion, particularly in the context of the Poisson distribution.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant introduces the problem of estimating the neutron flux λ based on the count N of detected neutrons, suggesting the use of maximum likelihood estimation.
  • Another participant confirms the relevance of the Poisson distribution in this context and inquires about the standard deviation in terms of λ.
  • A different participant states that the standard deviation for a Poisson distribution is the square root of λ but expresses uncertainty about its applicability to their specific situation.
  • Another participant suggests that to estimate an empirical variance, at least two measurements would be necessary, indicating a limitation in using a single measurement for variance estimation.

Areas of Agreement / Disagreement

Participants generally agree on the use of the Poisson distribution for this problem, but there is disagreement regarding the applicability of the standard deviation and the need for multiple measurements to estimate variance.

Contextual Notes

The discussion highlights limitations related to the assumptions of the Poisson distribution and the implications of having only one measurement for estimating variance.

Who May Find This Useful

Researchers and students in experimental physics, particularly those interested in statistical methods for estimating parameters from limited data.

Scatterer
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Hello people, I think the problem what I have is well known in experimental physics. Hope, somebody can helps me, thanks in advance. Here is:

There is a source of neutrons with a flux of λ neutrons per minute, which you do not know and want to estimate. You open the detector for one minute and it counts N neutrons. The maximum likelihood estimator for λ would be N.
Find the dispersion (or standard deviation) of this estimator. What will it be for the limiting case N=0?

Looks like Poisson distribution, where λ isn't known.
 
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Scatterer said:
Looks like Poisson distribution, where λ isn't known.

Yes, exactly. What is the standard deviation in terms of lambda for a Poisson distribution?
 
Standard deviation in terms of lambda is square root from lambda, but my event is different I think, have you any idea?
 
I think this is the best you can get with just one measurement. To estimate an empirical variance would require at least two measurements.
 

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