Log-logistic distribution

The log-logistic distribution is like a bell-shaped curve but stretched out a bit more and has a longer "tail". It's used to describe a situation where lots of things start off at low numbers but can reach very large numbers. Imagine a race with a very big starting line of lots of people, but then the fastest few people will be way ahead at the end. The log-logistic distribution shows this kind of situation, where lots of people will stay at a low level but some can reach high levels.