daily # of BTCs statistics

[jaybny]

Hey There,

a math question.

does anyone have any data on the distribution of #? i heard it is a Poisson distribution.. is it a based on a model? where is the randonmess? on what order?  what is lamda?

thanks
 

[Stephen Gornick]

Hey There,

a math question.

does anyone have any data on the distribution of #? i heard it is a Poisson distribution.. is it a based on a model? where is the randonmess? on what order?  what is lamda?

thanks
 

Are you referring to how many are issued each day?  The target is roughly 7,200 BTC (50 are issued with each block, and a block is generated roughly every 10 minutes).  The time between one block to the next can range far from the (approximate) 10 minute target -- from few seconds (very rare) to over an hour (also very rare).
  http://en.bitcoin.it/wiki/FAQ#How_are_new_Bitcoins_created?

There was an excellent site (nullvoid.org) that provided charts based on block generation data, including distribution, however the operator no longer offers the service due to, from my understanding, it requiring dedicated server resources.
  - http://bitcointalk.org/index.php?topic=527.0
  - http://bitcointalk.org/index.php?topic=402.0

[ribuck]

Lachesis has provided the details it in this post.

P(p,t)=1-e^(-pt)
Where p is the probability that you will win in one second: p=khps*1000*target/2^256, and t is the number of seconds.

So I solved for t:
t = -ln(1-P)/p

Llama agrees in this post.

To calculate average (expected value of generation time):

1/(pr)

To calculate how long until you have a T chance of producing at least 1 block:

-ln(1-T)/pr


Where:

p = probability of a given hash resulting in success (TARGET / 2^256)
r = rate in hashes / sec
T = target probability, such as 0.95
ln = log base e

What lachesis and llama call "target" is Bitcoin's hashing difficulty factor (currently 109670 but due to increase in the next day or so).