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:
\(R_n = \sqrt{\overline{X}^2 + \overline{Y}^2}\)
I think the third equation:
\(\bar X, \bar Y \sim N(0,\sigma^2/n)\)
should be:
\(\bar X, \bar Y \sim N(0,\frac{\sigma}{\sqrt{n}})\)
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.
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.
- 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)
- I don't want just a different notation, I want consistency in the notation. The top part uses R(n) which gets swizzled to \(R_n\) in the lower part. That sort of thing drives me crazy. :-(
