I have written similar tools

- for command line, fermi: https://git.nunosempere.com/NunoSempere/fermi

- for android, a distribution calculator: https://f-droid.org/en/packages/com.nunosempere.distribution...

People might also be interested in https://www.squiggle-language.com/, which is a more complex version (or possibly <https://git.nunosempere.com/personal/squiggle.c>, which is a faster but much more verbose version in C)

I like this!

In the grand HN tradition of being triggered by a word in the post and going off on a not-quite-but-basically-totally-tangential rant:

There’s (at least) three areas here that are footguns with these kinds of calculations:

1) 95% is usually a lot wider than people think - people take 95% as “I’m pretty sure it’s this,” whereas it’s really closer to “it’d be really surprising if it were not this” - by and large people keep their mental error bars too close.

2) probability is rarely truly uncorrelated - call this the “Mortgage Derivatives” maxim. In the family example, rent is very likely to be correlated with food costs - so, if rent is high, food costs are also likely to be high. This skews the distribution - modeling with an unweighted uniform distribution will lead to you being surprised at how improbable the actual outcome was.

3) In general normal distributions are rarer than people think - they tend to require some kind of constraining factor on the values to enforce. We see them a bunch in nature because there tends to be negative feedback loops all over the place, but once you leave the relatively tidy garden of Mother Nature for the chaos of human affairs, normal distributions get pretty abnormal.

I like this as a tool, and I like the implementation, I’ve just seen a lot of people pick up statistics for the first time and lose a finger.

https://www.getguesstimate.com/ is this, as a spreadsheet

I have made a similar tool but for the command line[1] with similar but slightly more ambitious motivation[2].

I really like that more people are thinking in these terms. Reasoning about sources of variation is a capability not all people are trained in or develop, but it is increasingly important.[3]

[1]: https://git.sr.ht/~kqr/precel

[2]: https://entropicthoughts.com/precel-like-excel-for-uncertain...

[3]: https://entropicthoughts.com/statistical-literacy

This is neat! If you enjoy the write up, you might be interested in the paper “Dissolving the Fermi Paradox” which goes even more on-depth into actually multiplying the probability density functions instead of the common point estimates. It has the somewhat surprising result that we may just be alone.

https://arxiv.org/abs/1806.02404