Thanks Max, you make a good point about differentiating between exponentials, Paretos, and log-normals. It does seem like log-normals are the norm when it comes to these skewed distributions, especially with things like world income. Still, keeping an open mind as to which of the skewed distributions best fits the data can hopefully make these models more robust.
You mentioned the challenges of distinguishing between these heavy-tailed distributions, and I would only add that this challenge increases when viewing these outcomes as intervals rather than points. For the sake of creating graphable data here, I only used the midpoint of the ranges listed on DCP3, but some of the intervals did span orders of magnitudes.
Finally, I’m not sure exactly what you mean about the complications of interpreting exponential distributions beyond some cutoff, but if the question was about applying the memoryless property to exponentials (and the tail only depending on the rate parameter), there’s a short derivation on Wikipedia. Again, not sure if that’s what you were getting at, but maybe it’ll clear things up.
Thanks Max, you make a good point about differentiating between exponentials, Paretos, and log-normals. It does seem like log-normals are the norm when it comes to these skewed distributions, especially with things like world income. Still, keeping an open mind as to which of the skewed distributions best fits the data can hopefully make these models more robust.
You mentioned the challenges of distinguishing between these heavy-tailed distributions, and I would only add that this challenge increases when viewing these outcomes as intervals rather than points. For the sake of creating graphable data here, I only used the midpoint of the ranges listed on DCP3, but some of the intervals did span orders of magnitudes.
Finally, I’m not sure exactly what you mean about the complications of interpreting exponential distributions beyond some cutoff, but if the question was about applying the memoryless property to exponentials (and the tail only depending on the rate parameter), there’s a short derivation on Wikipedia. Again, not sure if that’s what you were getting at, but maybe it’ll clear things up.
Thanks for the comments!