The idea's pretty simple. Your stories over the previous weeks will have some kind of distribution as to how long they each took. Let's say that the stories took this number of days each until the next story was finished:
3, 2, 5, 4, 1, 2, 3, 10, ...
These often follow something called a Weibull distribution, which is skewed towards a big, fat tail since most discoveries slow you down more than they speed you up. (Human intuition tends to assume a normal distribution, which is one of the reasons we're usually optimistic.)
Sometimes though these distributions are bimodal (there's some legacy system that slows down every story that touches it, for instance) or just plain messy (nobody checks in on a Friday because they don't want to break the build). The good thing about Montecarlo simulations is... it doesn't matter! It works regardless of what your distribution is.
The way you do it is to calculate a random journey through the stories you have left, and find when that journey finishes. So let's say I reckon I have 60 stories left. For each story, I'm going to pick how long it took between stories randomly from your distribution.
1, 5, 4, 10, 3, 2, 10, 2, 5...
And you keep doing this until all 60 stories are done. Now add the number of days it took to the starting date...
...and then do it again.
Do it 1000 times or more (yes, you'll need software for this, or a specialized spreadsheet). It doesn't matter if that weird "10" gets picked twice because that won't happen for every journey; some will be strangely slow, but most will be faster. Record the end-dates for each journey.
Now you have something more than an estimate. You have a probabalistic forecast. So if I start on 1st January 2018, I might get something like:
Each one of those dates shows what percentage of the journeys you took finished by that date. This gives you an idea of the probability of hitting any given date with all the stories. Alternatively, you can see how many stories you get done by a given date, just counting until the date is reached.
Most people are really optimistic when they estimate, and you're lucky if you even hit 50% of journeys finishing by that date!
Troy Magennis of Focused Objective has free spreadsheets for things like this, and Dan Vacanti at Actionable Agile's tool is cheap enough and IMO excellent. Both of them also have numerous videos talking about the technique. I also have an open source project that has no validation yet but works well enough for importing Excel spreadsheets, including exports from Jira.
Troy recommends between 7 and 25 weeks' worth of data to get this to work; more than that is usually out-of-date. Do bear seasonal patterns in mind, though.
If you don't want to go through the hassle of Montecarlo, but you do want the probability distribution, a technique I learned from Douglas Hubbard, author of "How to measure anything", might help you.
I ask the team to give me an idea of when they think they'll ship. Usually they'll be really optimistic, so if it's early January they'll say "End of April", or something like that.
Then I ask them how likely they are to ship then. "Oh, 70%," they tell me.
So I offer them a hypothetical prize of £10,000 and two different ways to win it. They can either choose a red marble from a bag containing 7 red and 3 white marbles, or they can ship by the end of April.
They usually go for the marbles; despite saying they're 70% certain to ship, they prefer the chances of drawing 7 out of 10 marbles!
So we reduce the number of marbles in our hypothetical bag until they prefer to ship. That tells us what their real confidence levels are. By doing this with different numbers of marbles, we can get a range of different confidence levels.
How to use these
If you're dependent on the shipping date in any way, don't use anything less than 85% confidence. That's usually way out compared to most people's estimates. As the date gets closer you'll be able to see if you're going to make it or not, and you will still have a chance to expedite things or shift other dependencies if required.
Note that the business will not be happy... until they start seeing the time saved by not estimating in easily-gameable story points, and by not having to redo a ton of plans based on something that was never going to happen anyway. You might need to do a bit of education or navigate tricky politics until they accept reality.