[Technical series]

The standard way of specifying statistical distributions is via their probability mass or probability density function, or via their distribution function, F(x) = P(X ≤ x).

This seminar is a guide to the distributions that can be defined by the inverse of the distribution function, the quantile function, Q(p), where Q(p)=x where x is the smallest x such that P(X ≤ x)=p.

There are theoretical and computational advantages to the quantile approach, which I will illustrate by introducing a number of different distributions, including the generalised lambda, the quantile defined skew logistic, and the logistic-exponential.