Optimal estimate of probability density functions from experimental data

TL;DR

This paper introduces an optimal method for estimating probability density functions from time series data, significantly improving accuracy over traditional histogram methods, especially for rare events.

Contribution

The proposed method provides near-arbitrary resolution PDFs from experimental data, outperforming standard histogram techniques in accuracy and detail.

Findings

Enhanced accuracy in estimating low-probability regions

Better resolution of PDFs from experimental data

Significant improvement over histogram methods

Abstract

A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When results are compared with PDFs of the same data calculated using the standard histogram method, a remarkable improvement is observed, especially in far lateral regions of the PDF, where low probability events give poor statistics.