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Comment by jakelarkin | Hacker News Reader

saved you a click:

time distribution follows a log-normal distribution (fat tail to the right)

statistically modeling pathogen progression over tissue spatially (2d, 3d) seems to confirm the real world distribution

The log-normal is an underappreciated distribution. It's almost as common as the normal distribution, and it shows up a lot in human-relevant stuff. For example, on the main page now is a bit about 'luck' where the model/simulation is clearly generating log-normal distributions and all the power-law stuff is a distraction; many things form a natural 'pipeline' where the normal variables multiply rather than sum, and so you get a log-normal. A famous example is Shockley's analysis of scientific productivity: https://www.gwern.net/docs/iq/1957-shockley.pdf If you are somewhat above-average in getting new ideas, in researching them, and in publishing them, say, you will wind up producing a lot more than someone who is just a little below-average across the board. Throw in a general factor like intelligence or just some inter-correlations, and the skew will be even more extreme.

For infections, multiplicativity makes a lot of sense. After all, what is an infection but a virus or bacteria literally being fruitful & multiplying? Small differences in immune system or the virus affecting its speed of reproduction or net total in each 'stage', and then a log-normal wouldn't be too surprising.

It's funny because towards the end of the article:

> As Scott and his colleagues noted in their paper, if a pathogen grows exponentially and a population receives a statistically normal distribution of exposures to it, then a lognormal distribution of incubation times should result

This makes it seem trivially obvious that you would expect a log normal distribution. I'm conflicted because I'm glad I read an interesting article, but why was it presented as if there were any surprise or mystery to it?

Things that are obvious to one person aren't to another.

Right, and it wasn't something that I knew before reading the article. I appreciate that. What I don't is that there's a fairly simple and likely reason those charts look the way they do. The article makes it seem like a miraculous and unexplained coincidence.

It does seem trivially obvious - if you are already closely familiar with the log-normal. :) I read the first few lines and thought, 'a long tail of infection times? Infections are based on exponential growth. I bet this is a log-normal!' This is because I like the log-normal and notice it, but it's not something which gets a lot of coverage or is routinely taught in statistical material.

A similar thing is the tail effects or order statistics of a normal distribution: if you set a cut off or threshold and look at the distribution of samples beyond it, it can look very surprisingly different from the original distribution. This comes up all the time in discussions of IQ, testing, higher education, racism/sexism/bias in general, health & disease, genetics, optimization etc, and keeps surprising the heck out of people because even though it's a statistical triviality, it's both counterintuitive and not typically taught.

Sorry, but why would you assume someone on Hacker News would want a click to be "saved"? This implies that the op is either clickbait or a waste of time.

I assume most of us aren't here for short-form Tweet-size chunks of information, but rather we want to know the details about things.

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