Statistical distribution of mining bitcoins?

[kseistrup]

Hi there,

Does anyone know which statistical distribution bitcoin mining is following?  I've been looking at the output from jgarzik's cpuminer, and I expected the “PROOF OF WORK RESULT: true (yay!!!)” lines to approximate a Poisson distribution (completely random, rare event).  Possion distributed data has same mean and variance, but the data I'm looking at has a variance of appr. mean².

Anyone?

Cheers,

[Cryptoman]

Yes, it's Poisson.

[kseistrup]

Yes, it's Poisson.

I beg to differ.  When I analyze the logfile from the cpuminer I get a mean (i.e., average time between delivering PoW) of appr. 1725 seconds with a variance of appr. 600E6 s².  The landmark of the poisson distribution is that its mean equals its variance.

Cheers,

[ArtForz]

It's poisson.
Remember, if events in a fixed timespan is poisson, time between events is a exponential distribution.

[kseistrup]

It's poisson.
Remember, if events in a fixed timespan is poisson, time between events is a exponential distribution.

Yes, you're right.  Except:  Even when I feed events/timeunit into the calculator, the variance is much higher than expected.  But perhaps I don't have enough data points…

Thanks for your input.

Cheers,