When Life isn't Gaussian: The Allan Deviation Family of Statistics

When analyzing data, it is common to assume a Gaussian distribution of noise around a "true" mean value. But real life often isn't Gaussian, so how do we deal with other kinds of noise? How do we think about data that does not have a well-defined mean? The Allan deviation family of statistics offers a series of tools to address these problems. Originally developed for characterizing the performance of oscillators, the family of statistics is now a mainstay of all kinds of time and frequency measurement and has found a growing range of applications across fields. In this presentation, I give a brief introduction to the Allan variance, highlight some other related statistics, and show their use in a variety of problem areas. I provide example code in Python and suggest a starting point for exploring these concepts with simulation.