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I noticed an oddity in the definition of the circular variance, which probably has historical reasons: While it is not generally true that the estimator of the circular standard deviation squared yields the circular standard deviation, I would have expected this equality to hold for very small
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The current title of this article is directional statistics, which is a synonym of circular statistics. A quick search on Google
Scholar and Google Books will show that the latter term, "circular statistics," is more widely used than "directional statistics". Here are the results.
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Consider the same example but rotated further to the left so that the three angles are 330, 340 and 350 degrees. Taking the modulus 360 of the sum (1020) results in 2 remainder 280, which divided by 3 is clearly not 340.
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values of the circular standard deviation, which recovers the linear case. However, there is a factor of 2 missing! You can test this numerically yourself with the following line of code
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I've added the wrapped normal distribution as an example of the way a wrapped distribution can be made from the pdf of another distribution. I'm also redirecting the nonexistent
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The final step of the formula given for the example is unclear; apparently it is written for result in radians. Wouldn't it be better written this way:
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Mean angle = arctangent (mean sine / mean cosine). If mean cosine < 0, add 180 degrees to the result. If mean sine <0 and mean cosine : -->
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Agreed - I've removed it. Also, this article is about
Directional statistics itself, not about various methods to calculate a circular average.
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As the remainder (in a modulus 360 operation) can only range from 0 to 360, the 'average' can only range from 0 to 360/n.
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N ( \mu ,\sigma^2) round the circle gives the wrapped normal distribution W N ( \mu , rho )
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Thus, I would like to propose renaming this article to
Circular statistics. Any thoughts?
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439:"Circular statistics": 9,670 results on Google Scholar and 811 results on Google Books
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with \rho = exp{ -\sigma^2/2) as in (3.5.63), so that 1 - \nu =\exp(- \sigma^2 / 2 ).
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The modulus method only works in few specific cases (such as the example given).
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I started a new
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Unless I'm misunderstanding the procedure, I would suggest taking it out.
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std_circ=sqrt(-2*log(abs(mean(exp(1i*sigma*randn(1e5,1))))))
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I therefore added the following sentence to the article:
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For small \nu, (3.4.14) reduces to \sigma = \sqrt(2\nu).
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161:var_circ=1-abs(mean(exp(1i*sigma*randn(1e5,1))))
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255:{\displaystyle S(z)^{2}=2\mathrm {Var} (z)}
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193:{\displaystyle S(z)}
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