A Statistical Prescription to Estimate Properly Normalized Distributions of Different Particle Species

TL;DR

This paper introduces a data-driven statistical method to accurately estimate normalized distributions of different particle species, accounting for dependencies on unknown kinematic variables without prior assumptions.

Contribution

The paper presents a novel, unbiased, and fully data-driven approach to estimate particle distributions considering variable dependencies, improving upon traditional methods.

Findings

Provides a bias-free estimation technique

Ensures proper normalization of distributions

Applicable to any kinematic distribution

Abstract

We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions are unknown and different for each particles species. We show that the proposed procedure provides properly normalized and completely data-driven estimation of the unknown distributions without any a priori assumption on their functional form. Moreover, we demonstrate that the method can be generalized to any kinematical distribution of the particles.