What Is a Rayleigh Distribution?

The Rayleigh distribution is the distribution of the magnitude of a two-dimensional random vector whose coordinates are independent and identically distributed with mean zero normal variables. It is named for William Strutt, who is also known as Lord Rayleigh.

A Rayleigh distribution is often observed when the overall magnitude of a vector is related to its directional components. One way that the Rayleigh distribution naturally arises is when wind velocity is analyzed in its orthogonal two-dimensional vector components. The overall wind speed, which is known as vector magnitude, is characterized by a Rayleigh distribution when each component is uncorrelated and normally distributed with equal variance and zero mean.