WillNickols

Charitable Giving and the Exponential Distribution

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!

Charitable Giving and the Exponential Distribution

Really interesting, thanks for pointing this out!

Thanks for the questions!

Yes, "average" means "mean" throughout.

I calculated those estimates with a LOTUS (population weighted average) approach: multiplying the population's probability of dying at each age by that age itself and taking the sum of those products from ages 0 to infinity. In practice, I took the sum of the products from ages 0 to 1 million because the probability of living past 1 million was so low in these models that there was no contribution to the sum that was more than R's round-to-zero threshold.

And though none of these models account for it, it does seem like the risk of dying from homicide and suicide ought to decrease with age as society presumably finds life more valuable.

For reference, the median age of death for these are as follows:

As expected, for all the right-skewed models (everything except reality), the median is less than the mean.