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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).

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AI Impacts used a Gamma distribution here: