The multivariate probability integral transform

**Hora de inicio:** 12:00. **Hora de fin:** 13:00.

It is well-known from elementary probability theory that, if X is a random variable on a given probability space and if its distribution function F is continuous, then the random variable X = F(X) is uniformly distributed on [0,1]. This is called the probability integral transform (shortly, PIT) of X. In higher dimensions, however, the PIT is a much richer tool that is also far less understood. In this talk, we present the basic properties of multivariate PIT and discuss a recent application to the determination of a suitable notion of quantile for multivariate random vectors. Practical examples are given about the use of PIT as measure of risk for multivariate events in hydrology.