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

In summary, The conversation discusses the problem of estimating the flux of neutrons from a source in experimental physics. The maximum likelihood estimator for the flux is N, but the dispersion or standard deviation of this estimator is unknown. It is believed to follow a Poisson distribution, but more measurements are needed to estimate the variance.
  • #1
Scatterer
2
0
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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  • #2
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?
 
  • #3
Standard deviation in terms of lambda is square root from lambda, but my event is different I think, have you any idea?
 
  • #4
I think this is the best you can get with just one measurement. To estimate an empirical variance would require at least two measurements.
 

1. What is the purpose of calculating the dispersion of the estimator of neutron flux number?

The dispersion, also known as the standard deviation, of the estimator of neutron flux number is used to measure the variability or spread of the estimated neutron flux values around the mean. This helps to assess the precision and accuracy of the estimator and determine the reliability of the results.

2. How is the dispersion of the estimator of neutron flux number calculated?

The dispersion is calculated by taking the square root of the variance of the estimator. The variance is obtained by summing the squared differences between each estimated value and the mean, and then dividing by the total number of values.

3. What factors can affect the dispersion of the estimator of neutron flux number?

The dispersion can be affected by various factors, such as the quality of the data used for estimation, the accuracy of the measurement tools, and the precision of the calculation methods. Additionally, any errors or biases in the estimation process can also contribute to the dispersion.

4. How does a high dispersion of the estimator of neutron flux number affect the reliability of the results?

A high dispersion indicates a large spread of values around the mean, which can suggest that the estimator is not precise and that the estimated values may vary significantly. This can decrease the reliability of the results and make it difficult to draw accurate conclusions based on the estimated neutron flux values.

5. Can the dispersion of the estimator of neutron flux number be reduced?

Yes, the dispersion can be reduced by improving the quality of the data and measurement tools, using more accurate and precise calculation methods, and minimizing any errors or biases in the estimation process. Regular calibration and validation of the estimation methods can also help to reduce the dispersion and improve the reliability of the results.

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