Difference between revisions of "Talk:Sighter Distribution"
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| − | I think the third equation:<br /> | + | <strike>I think the third equation:<br /> |
<math>\bar X, \bar Y \sim N(0,\sigma^2/n)</math><br /> | <math>\bar X, \bar Y \sim N(0,\sigma^2/n)</math><br /> | ||
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should be:<br /> | should be:<br /> | ||
| − | <math>\bar X, \bar Y \sim N(0,\frac{\sigma}{\sqrt{n}})</math><br /> | + | <math>\bar X, \bar Y \sim N(0,\frac{\sigma}{\sqrt{n}})</math><br /></strike> |
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| + | :: Huh?? Evidently the standard is to use variance not standard deviation. So the suggestion is wrong.<br />[[User:Herb|Herb]] ([[User talk:Herb|talk]]) 19:31, 31 May 2015 (EDT) | ||
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<math>f_{R_n}(r_n)</math> | <math>f_{R_n}(r_n)</math> | ||
| − | seems it should just be something like '''If <math>C | + | seems it should just be something like '''If <math>C</math> is the position of the true center relative to the experimental center <math>C^*</math> <math>(\overline{X}, \overline{Y})</math>, then the probability density function of <math>C^*</math> is:<br />''' |
<math>PDF({C^*})= </math> yada yada | <math>PDF({C^*})= </math> yada yada | ||
which would also require changing <math>r_n</math> to <math>R_n</math> in equation. | which would also require changing <math>r_n</math> to <math>R_n</math> in equation. | ||
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| − | [[User:Herb|Herb]] ([[User talk:Herb|talk]]) | + | |
| + | : '''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. [[User:David|David]] ([[User talk:David|talk]]) 21:03, 1 June 2015 (EDT)''' | ||
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| + | :: I don't want just a ''different'' notation, I want consistency in the notation. The top part uses R(n) which gets swizzled to <math>R_n</math> in the lower part. That sort of thing drives me crazy. :-( | ||
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| + | :: I'll fix this to my liking and then let you have a chance to throw up on it... :-)<br />[[User:Herb|Herb]] ([[User talk:Herb|talk]]) 23:31, 1 June 2015 (EDT) | ||
Latest revision as of 23:31, 1 June 2015
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. :-(
