critband: A Python Package for Critical Bandwidth Analysis of Multimodal Distributions

TL;DR

critband is a Python package that efficiently detects bimodality in multimodal distributions using Silverman's kernel density approach, filling a gap in the Python ecosystem.

Contribution

It introduces a comprehensive Python tool for critical bandwidth bimodality detection with advanced features and improved performance over existing R tools.

Findings

Stable bimodality detection for well-separated cases

Expected instability in boundary cases

3-10 times faster than R's modetest()

Abstract

Multimodal density estimation is a fundamental problem in scientific computing. Determining the number of modes in a distribution is a core numerical challenge with applications across ecology, economics, genomics, and astronomy. While the R ecosystem provides mature tools through the multimode package, the Python ecosystem has lacked an equivalent cohesive implementation. We present critband, a Python package for critical bandwidth bimodality detection based on Silverman's kernel density approach. The package implements critical bandwidth search with a robust bracketed mode-count solver and FFT-accelerated KDE, and provides additional features including k-mode detection, component decomposition, bimodality strength quantification, and excess mass estimation. Validation against twelve benchmark cases spanning separation regimes, unequal variances, unequal weights, and small sample sizes shows stable estimates for clearly separated cases and expected instability for boundary cases. Performance benchmarks show critband is typically 3-10 times faster per case than R's modetest() in the tested setup.