Asymptotic distribution of the statistical complexity under the multinomial law

Abstract

The Statistical Complexity is a feature computed from a probability function that aims to quantify the structure of the system that produced the observations. It is the product between the normalized Shannon Entropy and the normalized Jensen–Shannon distance between the probability function and the uniform law. We obtain the Statistical Complexity asymptotic distribution under the Multinomial model, and we validate this result with numerical experiments. We present examples where this asymptotic result provides a good approximation, even in scenarios where the Multinomial model is not strictly valid, such as in applications to Bandt and Pompe ordinal patterns. We provide the R code that implements these functions.