Calculating 95% confidence interval of block find time

[Bitmong]

Hello,

I know how to calculate the average time to find a block given a hash rate and difficulty.

However, I would like to calculate the 95% confidence interval on the time to find a block. That is, with 95% certainty the block is found in x +- y minutes, where x is the average and y is the 95% limit.

How is that calculated?

[Bitmong]

Anyone?

[kslavik]

Your average time to find a block is 50% confidence.
For 75% (50%+25%) confidence, the time is 2x of the average time to find a block.
For 87.5% (50%+25%+12.5%) confidence, the time is 3x of the average time to find a block.
For 93.75% (50+25+12.5+6.25) confidence, the time is 4x of the average time to find a block.
for 96.875% (50+25+12.5+6.25+3.125) confidence, the time is 5x of the average time to find a block.

I think this is how it works. I'm pretty sure you can come up with a formula based on those numbers.

[grue]

http://www.alloscomp.com/bitcoin/old_calculator.php

if you look at the source, you have:

  var rate = your rate
  var target = 0x00000000ffff0000000000000000000000000000000000000000000000000000 / your difficulty
  var p = target*rate*1000/Math.pow(2,256);
  var result = (-Math.log(1-your confidence interval in decimal)/p)

where result is in seconds