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I'm pretty sure that this is the same math we played with in Re: [OT] The statistics of hashing.. I don't know how to compute the standard deviation, though. I'll have to do a bit of reading and see what I can come up with. But judging from the results from that thread, I'd expect there to be minimal overlap between two sets of 1e6 bits in 4e9 possibilities.

Update: I found my script, but since I'm on a 32-bit machine, I couldn't run it with 2^32 bit vectors. (I really need to stand up a 64-bit OS and perl one day.) But I ran it with a million samples in a pair of vectors of various sizes (2^24, 2^26, 2^28, 2^30 and 2^31) and it looks like collisions shouldn't be very frequent, judging from the progression:

$ ./ 24 2 1000000 N=16777216, V=2, X=1000000 integral(1000000)=25166956.740071, integral +(0)=25165824 Expected collisions: 1132.74007095024 $ ./ 26 2 1000000 N=67108864, V=2, X=1000000 integral(1000000)=100663369.193409, integra +l(0)=100663296 Expected collisions: 73.1934093236923 $ ./ 28 2 1000000 N=268435456, V=2, X=1000000 integral(1000000)=402653188.613027, integr +al(0)=402653184 Expected collisions: 4.61302703619003 $ ./ 30 2 1000000 N=1073741824, V=2, X=1000000 integral(1000000)=1610612736.28892, integ +ral(0)=1610612736 Expected collisions: 0.288918733596802 $ ./ 31 2 1000000 N=2147483648, V=2, X=1000000 integral(1000000)=3221225472.07225, integ +ral(0)=3221225472 Expected collisions: 0.0722546577453613


When your only tool is a hammer, all problems look like your thumb.

In reply to Re: [OT] Statistics question. by roboticus
in thread [OT] Statistics question. by BrowserUk

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