What is Bitcoin block time ditribution?

[Frodek]

Here are times of last generated blocks:
383646 2015-11-15 09:21:46 7.05
383645 2015-11-15 09:14:43 7.28
383644 2015-11-15 09:07:26 20.28
383643 2015-11-15 08:47:09 13.97
383642 2015-11-15 08:33:11 13.78
383641 2015-11-15 08:19:24 44.22
383640 2015-11-15 07:35:11 7.40
383639 2015-11-15 07:27:47 7.57
383638 2015-11-15 07:20:13 21.25
383637 2015-11-15 06:58:58 38.05
383636 2015-11-15 06:20:55 25.03
383635 2015-11-15 05:55:53 0.53
383634 2015-11-15 05:55:21 4.15
383633 2015-11-15 05:51:12 0.72
383632 2015-11-15 05:50:29 2.40
383631 2015-11-15 05:48:05 14.55
383630 2015-11-15 05:33:32 10.85
383629 2015-11-15 05:22:41    //17 from top
383628 2015-11-15 05:03:16
383627 2015-11-15 05:11:19    //05:11:19 is greater than 05:03:16 - time can be negative?!
383626 2015-11-15 04:54:41
..
383594 2015-11-15 00:07:13   //52 from top

239.08/17=14.06
554.55/(383646-383594=52) = 10.66

I see that one block can have very different time - from 0.53 minutes to 44.22 minutes at this example, but over 50 blocks have very close to 10 minutes.
What is Bitcoin block time distribution? Poisson distribution? but Poisson is discrete, Normal? but normal don't distinguish left side from right (this distribution reaches right side more far than left?)
And warning 05:11:19 is greater than 05:03:16 - time can be negative?!
What is distribution single blocks and what group of blocks, for example 4, 50 or 2016?

[ranochigo]

Bitcoin blocks are on average, 10 minutes intervals and difficulty is adjusted to achieve this. But however, variance can cause blocks to be seconds apart or even hours apart. Miners can choose their time stamp. It is valid if it is greater than the median time of the previous 11 blocks and less than 2 hours from the network adjusted time.

"Network-adjusted time" is the median of the timestamps returned by all nodes connected to you.

from https://en.bitcoin.it/wiki/Block_timestamp

[Frodek]

Aha, this explains why time is not greater.
But what is variance?
two problems:
a) i want generate random numbers from 1 to 45 which are distributed like time of bloks
b) what percent blocks have time <1minute or <40 minutes ?
    what percent blocks have time <9 or <11 minutes ?

[poncom]

This quote states Bitcoin block time distribution is exponential but it doesn't provide any mathematicalevidence to prove that it is. However, the quote explains the negative time difference between blocks is due to inaccurate timestamps. Apparently miners can use timestamps that bare no relation to the real time.

Excluding complications like difficulty changes and temporary blockchain splits, you can model the block generation time as an exponential distribution.

An exponential distribution has a standard deviation equal to the expectancy value. This predicts a 10 minute standard deviation for Bitcoin.

Measuring the actual distribution isn't that easy. While each block contains a timestamp, that timestamp isn't very accurate, and sometimes the time difference between blocks is even negative.
The timestamp doesn't change over the course of a single share, and some miners deliberately use timestamps deviating from the actual time