My distribution has median 2030ish. That means it peaks a bit before then, and then has a long tapering tail.

I'm fairly confident in this, because I've done lots of thinking and research about it. I have talked to smart experts who disagree and think I could maybe even pass an ITT for them. That said, they could probably pass an ITT for me too.

I think that the best available starting point is the Cotra / OpenPhil report on biological anchors.

Personally I treat this as an upper bound on how much compute it might take, and hold the estimates of when compute will become available quite lightly. Nonetheless, IMO serious discussion of timelines should at least be able to describe specific disagreements with the report and identify which differing assumptions give rise to each.

Log-normal is a good first guess, but I think its tails are too small (at both ends).

Some alternatives to consider:

• Erlang distribution (by when will k Poisson events have happened?), or its generalization, Generalized gamma distribution
• Frechet distribution (what will be the max of a large number of i.i.d. samples?) or its generalization, Generalized extreme value distribution
• Log-logistic distribution (like log-normal, but heavier-tailed), or its generalization, Singh–Maddala distribution

Of course, the best Bayesian forecast you could come up with, derived from multiple causal factors such as hardware and economics in addition to algorithms, would probably score a bit better than any simple closed-form family like this, but I'd guess literally only about 1 to 2 bits better (in terms of log-score).

A mixture of log-normals.

It looks like normal distribution around some mean value (2040+-10) is typically assumed, but it wrong, as obviously AGI probability is growing exponentially.

So some exponential distribution is needed, in which mean value is not far from unity. E.g.: 10 percent for 2030, 50 percent for 2035 and 99 percent for 2040.