Talk:Sighter Distribution

I think there is some slop in the equations that needs fixing.

I think the second equation:

\(R(n) = \sqrt{\overline{x_i}^2 + \overline{y_i}^2}\)

should be:

\(R_n = \sqrt{\overline{X}^2 + \overline{Y}^2}\)

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I think the third equation:

\(\bar X, \bar Y \sim N(0,\sigma^2/n)\)

should be:

\(\bar X, \bar Y \sim N(0,\frac{\sigma}{\sqrt{n}})\)

Huh?? Evidently the standard is to use variance not standard deviation. So the suggestion is wrong.
Herb (talk) 19:31, 31 May 2015 (EDT)

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There is another fine point that should be explicitly stated. The sample of three shots uses n as sample size. But the \(\sigma\) is the population standard deviation, not the sample standard deviation s.

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Don't really like this

\(f_{R_n}(r_n)\)

seems it should just be something like If \(C\) is the position of the true center relative to the experimental center \(C^*\) \((\overline{X}, \overline{Y})\), then the probability density function of \(C^*\) is:
\(PDF({C^*})= \)  yada yada

which would also require changing \(r_n\) to \(R_n\) in equation.

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Herb (talk) 15:14, 30 May 2015 (EDT)

The proof takes σ as given and solves for the distribution as a function of σ and n. There is no sample σ involved in the proof. Yes, the Normal here is parameterized by variance, not standard deviation. If you want to rewrite the proof using a different notation for the distribution I guess you can give it a shot. David (talk) 21:03, 1 June 2015 (EDT)