Asymmetric Statistical Errors

TL;DR

This paper discusses how to properly combine asymmetric statistical errors from finite sample maximum likelihood estimates, providing methods for single and multiple result aggregation with approximate parabolic parametrizations.

Contribution

It introduces methods for combining asymmetric errors from maximum likelihood estimates, addressing both single and multiple result scenarios with approximate parabolic curve parametrizations.

Findings

Proposes methods for combining asymmetric errors on a single measurement.

Provides techniques for aggregating multiple measurements with asymmetric errors.

Analyzes parametrization approaches for approximately parabolic likelihood functions.

Abstract

Asymmetric statistical errors arise for experimental results obtained by Maximum Likelihood estimation, in cases where the number of results is finite and the log likelihood function is not a symmetric parabola. This note discusses how separate asymmetric errors on a single result should be combined, and how several results with asymmetric errors should be combined to give an overall measurement. In the process it considers several methods for parametrising curves that are approximately parabolic.