# Robust Lifetime Estimation from HPGe Radiation-Sensor Time Series Using Pairwise Ratios and MFV Statistics

## TL;DR

This paper introduces a robust method for analyzing HPGe detector data using pairwise ratios and MFV statistics to accurately estimate decay lifetimes.

## Contribution

The novel approach uses pairwise ratios and the MFV statistic to reduce parameter correlations and improve robustness in decay analysis.

## Key findings

- Pairwise ratios eliminate amplitude–lifetime correlation in HPGe decay data.
- MFV statistics effectively summarize heavy-tailed lifetime estimates.
- The method yielded a precise lifetime of 4.0959±0.0007stat±0.0110syst days for 97Ru.

## Abstract

High-purity germanium (HPGe) gamma-ray detectors are core instruments in nuclear physics and astrophysics experiments, where long-term stability and reliable extraction of decay parameters are essential. However, the standard exponential decay analyses of the detector time-series data are often affected by the strong correlations between the fitted parameters and the sensitivity to detector-related fluctuations and outliers. In this study, we present a robust analysis framework for HPGe detector decay data based on pairwise ratios and the Steiner’s most frequent value (MFV) statistic. By forming point-to-point ratios of background-subtracted net counts, the dependence on the absolute detector response is eliminated, removing the amplitude–lifetime correlation that is inherent to conventional regression. The resulting pairwise lifetime estimates exhibit heavy-tailed behavior, which is efficiently summarized using the MFV, a robust estimator designed for such distributions. For the case study, a long and stable dataset from an HPGe detector was used. This data was gathered during a low-temperature nuclear physics experiment focused on observing the 216 keV gamma-ray line in 97Ru. Using measurements spanning approximately 10 half-lives, we obtain a mean lifetime of τ=4.0959±0.0007stat±0.0110syst d, corresponding to a half-life of T1/2=2.8391±0.0005stat±0.0076syst d. These results demonstrate that the pairwise–MFV approach provides a robust and reproducible tool for analyzing long-duration HPGe detector data in nuclear physics and nuclear astrophysics experiments, particularly for precision decay measurements, detector-stability studies, and low-background monitoring.