Difference between revisions of "Talk:Sighter Distribution"

From ShotStat
Jump to: navigation, search
 
Line 36: Line 36:
 
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.  
 
----
 
----
[[User:Herb|Herb]] ([[User talk: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. [[User:David|David]] ([[User talk:David|talk]]) 21:03, 1 June 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. [[User:David|David]] ([[User talk:David|talk]]) 21:03, 1 June 2015 (EDT)'''
Line 42: Line 41:
 
:: 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. :-(
 
:: 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. :-(
  
:: I'll fix this to my liking and then let you have a chance to throw up on it... :-)<br />
+
:: 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:

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

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

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. :-(
I'll fix this to my liking and then let you have a chance to throw up on it... :-)
Herb (talk) 23:31, 1 June 2015 (EDT)