[1] It was introduced by Ole Barndorff-Nielsen, who studied it in the context of physics of wind-blown sand.

[3] An important point about infinitely divisible distributions is their connection to Lévy processes, i.e. at any point in time a Lévy process is infinitely divisibly distributed.

However, a Lévy process that is generalised hyperbolic at one point in time might fail to be generalized hyperbolic at another point in time.

It is mainly applied to areas that require sufficient probability of far-field behaviour[clarification needed], which it can model due to its semi-heavy tails—a property the normal distribution does not possess.

The generalised hyperbolic distribution is often used in economics, with particular application in the fields of modelling financial markets and risk management, due to its semi-heavy tails.