If I understand your question right, I think you're looking for the inverse cumulative distribution function (a.k.a. quantile function) of the Erlang distribution.
The random length of time to mine the next block has an exponential distribution with rate parameter 1/t. The length of time to mine n blocks has an Erlang distribution with shape parameter n and rate parameter 1/t.
The Erlang distribution is a special case of the Gamma distribution. The Erlang distribution's shape parameter must be an integer, but the Gamma distribution's shape parameter can be any positive real number. We can use the Gamma distribution if Erlang isn't given to us by our calculator.
The results of this simulation match the closed-form computation:
R
t <- 120
n <- 15
p <- 0.4
set.seed(314)
mining.times <- matrix(rexp(n * 100000, rate = 1/t), ncol = n)
mining.times <- rowSums(mining.times)
quantile(mining.times/n, probs = p)
qgamma(p = p, shape = n, rate = 1/t)/n
# Divide by n to get the mean instead of the total
Sometimes Trocador when I need to pay for something that doesn't accept Monero. If you use the ref-link in the monero.town sidebar it also helps fund the site without swaps costing any extra!
Decentralized reputation is not a thing. Every single approach can easily be gamed by scammers. Bisq2 requires people to buy thousands of $bsq for reputation.
Reto has been working pretty well for me. Sure, startup can take a while but I've heard they are migrating all the seednodes to tor pow which should help with the ddos attacks.
Partially. For the Monero blockchain itself this is basically it but the spam also enabled them to withdraw funds ($300k) from darknet markets multiple times in a row, since their withdrawal systems didn't account for transactions being this delayed.
Yeah sorry, I had not considered draining market wallets as an option. Thanks for the pentest, it greatly pushed FCMPs and high-throughput research forward!
They made money through extortion, not by draining any wallets due to spam. There was spam and it did delay transactions for regular users due to existing wallet bugs that are now fixed. I can't really comment on badly coded markets, I assume they somehow broke their payment systems because they didn't account for long delays when receiving coins or also had the fee selection bug.
Reply by rucknium:
If I understand your question right, I think you're looking for the inverse cumulative distribution function (a.k.a. quantile function) of the Erlang distribution.
The random length of time to mine the next block has an exponential distribution with rate parameter
1/t
. The length of time to minen
blocks has an Erlang distribution with shape parametern
and rate parameter1/t
.The Erlang distribution is a special case of the Gamma distribution. The Erlang distribution's shape parameter must be an integer, but the Gamma distribution's shape parameter can be any positive real number. We can use the Gamma distribution if Erlang isn't given to us by our calculator.
You would compute
T
in the R language with:The results of this simulation match the closed-form computation: