Talk:Central limit theorem for directional statistics

So what is the theorem?
At no place in the article, there is a statement of the theorem. Which expression, precisely, converges in distribution against which distribution?

Moreover, it seems that the article only treats the application of the bivariate case of the ordinary CLT to data on the circle. It would be nice to have a statement for the distribution of the unit-length normalized mean vector instead. Wurzel33 (talk) 13:23, 29 November 2013 (UTC)

Rn=1?
Isn't Rn=1? If so, what is the use to keep track of Rn? — Preceding unsigned comment added by 129.7.128.204 (talk) 15:34, 1 April 2015 (UTC)

Mie scattering example?
I was wondering the other day about how fog will scatter light toward the eye, and learned a lot about Mie scattering. It's somewhat complicated to calculate the Mie scattering distribution for a single particle, even for a simple sphere, but I wondered if maybe the average of many sequential Mie scattering events would be much simpler, tending toward a Gaussian because of the central limit theorem. I haven't really found anything about it yet, except for this article which I think suggests that my supposition is correct. I'm imagining an experiment where you hit a target (such as a suspension of particles in liquid) with a laser and look at the angular distribution of the Mie-scattered light coming out.

Anyways, it seems pretty straight forward to imagine, and I've done enough haze measurements and modeling to know how spatially structureless it is. So at least I'm sure that the sequential Mie-scattering distribution will on average be simpler than that of Mie scattering from a single particle. Maybe it would be Lambertian instead of Gaussian. Maybe the polarization of the input beam would produce some slight angular structure in the averaged output. Maybe subsequent Mie-scattering events cannot be thought of as added quantities as the central limit theorem requires. 2603:8080:1000:39AC:CDE4:3796:C576:6794 (talk) 04:43, 13 May 2024 (UTC)