Talk:Cantor distribution

Funny distribution this one, but nmot as funny as the word "eventuate" that was in the previous version of the article. --Lucas Gallindo 03:16, 5 October 2006 (UTC)

From the Oxford English Dictionary:

“ 2. To be the issue; to result, come about.

1834 DE QUINCEY Coleridge Wks. (1863) II. 93 In the upshot, this conclusion eventuated (to speak Yankeeishly), that, etc. 1876 C. M. DAVIES Unorth. Lond. I. 25 If So-and-so were condemned, a schism in the National Church would eventuate. 1884 Law Times 14 June 121/1 When there was danger of a war eventuating with America.

”

Michael Hardy 16:11, 5 October 2006 (UTC)

Alternate definition?

Is this distribution also the limiting (as n goes to infinity) distribution of

${\frac {1}{2}}+\sum _{i=1}^{n}{\frac {R_{i}}{3^{i}}},\,\!$

where the R_i are iid Rademacher distributions? Seems to me that it is, but my proof skills are quite rusty... Baccyak4H (Yak!) 20:15, 12 December 2006 (UTC)

• Since any number in the Cantor set can be (uniquely) expressed, in base 3, as 0.abcd... where a,b,c,d,... are either 0 or 2, then a simple way to simulate this Cantor distribution would be to add iid Bernoullis, scaled to 2/3:

$\sum _{i=1}^{n}{\frac {2}{3^{i}}}B_{i}({\frac {1}{2}})\,$

Since Rademacher and Bernoulli are essentially the same distribution, just scaled ($R_{i}=2B_{i}({\frac {1}{2}})-1\,$), then a simple substitution could prove your expression. Albmont (talk) 20:21, 17 July 2008 (UTC)

• BTW, I think the characteristic function of the Cantor distribution is wrong. It seems like a series that diverges everywhere. Albmont (talk) 20:21, 17 July 2008 (UTC)