Difference between revisions of "Talk:Derivation of the Rayleigh Distribution Equation"
(Created page with "''' rev 13:28, 3 June 2015 Herb ''' Ok, name of page needs a bit of fixing. more verbosity in text I goofed in accuracy section. "PDF" functions are set up wrong. Shoul...") |
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| + | This is topic that I think bears further investigation... | ||
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| + | is it <math>\sigma_h = \sigma_v</math> or <math>\sigma_h^2 = \sigma_v^2</math> ?? | ||
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| + | Of course if they are equal then both equations are true. The problem is in pooling the values if:<br /> | ||
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| + | <math>\sigma_h \approx \sigma_v</math> | ||
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| + | which equation do we use to pool the values? | ||
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| + | * <math>(\sigma_h + \sigma_v)/2</math> | ||
| + | * <math>\sqrt{\sigma_h^2 + \sigma_v^2}</math> | ||
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| + | I think <math>\sqrt{\sigma_h^2 + \sigma_v^2}</math> should be corrected by factor <math>\frac{1}{\sqrt{2}}</math> since <math>(\sigma + \sigma)/2 = \sigma</math> but <math>\sqrt{\sigma^2 + \sigma^2} = \sigma \sqrt{2}</math> | ||
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| + | In general it would seem that the ratio <math>(\sigma_h / \sigma_v)</math> could be useful as a guide to stay out of trouble. Obviously the ration should depend on sample size, ''n''. but something like <math> .66\sigma \leq (\sigma_h / \sigma_v) \leq 1.5\sigma </math> is the idea... | ||
Revision as of 14:48, 3 June 2015
rev 13:28, 3 June 2015 Herb
Ok, name of page needs a bit of fixing.
more verbosity in text
I goofed in accuracy section. "PDF" functions are set up wrong. Should be something like "PDF of X as x"
Been about 45 years since I took calculus in college. I'll have to look up conversion from Cartesian to Polar coordinates, but I know the conversion will swizzle to the right answer...
This is topic that I think bears further investigation...
is it \(\sigma_h = \sigma_v\) or \(\sigma_h^2 = \sigma_v^2\) ??
Of course if they are equal then both equations are true. The problem is in pooling the values if:
\(\sigma_h \approx \sigma_v\)
which equation do we use to pool the values?
- \((\sigma_h + \sigma_v)/2\)
- \(\sqrt{\sigma_h^2 + \sigma_v^2}\)
I think \(\sqrt{\sigma_h^2 + \sigma_v^2}\) should be corrected by factor \(\frac{1}{\sqrt{2}}\) since \((\sigma + \sigma)/2 = \sigma\) but \(\sqrt{\sigma^2 + \sigma^2} = \sigma \sqrt{2}\)
In general it would seem that the ratio \((\sigma_h / \sigma_v)\) could be useful as a guide to stay out of trouble. Obviously the ration should depend on sample size, n. but something like \( .66\sigma \leq (\sigma_h / \sigma_v) \leq 1.5\sigma \) is the idea...
