A pitfall in the use of extended likelihood for fitting fractions of pure samples in mixed samples

TL;DR

The paper identifies a subtle analytic mistake in the use of extended likelihood methods for estimating pure sample fractions, which impacts error estimates in widely used software.

Contribution

It reveals a common error in applying extended likelihood to mixed sample analysis and demonstrates its effect on error estimation.

Findings

The mistake affects error estimates in software packages.

Correct application is crucial for accurate fraction determination.

The paper provides guidance to avoid this pitfall.

Abstract

The paper elucidates, with an analytic example, a subtle mistake in the application of the extended likelihood method to the problem of determining the fractions of pure samples in a mixed sample from the shape of the distribution of a random variable. This mistake, which affects two widely used software packages, leads to a misestimate of the errors.