[hackinthebochs]

>without specifying its pdf or how you could derive the pdf

Would you or anyone happen to know of a good book that discusses the derivation of various advanced probability distributions? It is quite frustrating that every ML or stats book I come across run through various distributions without giving the reader any sort of motivation or intuition behind them. Without that intuition how am I supposed to have any idea when to apply one vs another?

[mariuskempe]

I honestly can't recommend a book for this. The best resource I've found is MathWorld. I've picked up a bunch of very helpful intuitions from it, including:

- Cauchy: the horizontal distance from the origin at which an arrow shot at a random angle from a point below the origin hits the x-axis

- Gamma: how long you have to wait for the nth event in a Poisson process

I'm sure these must be books that I haven't read.