Maximum-likelihood analysis and goodness-of-fit estimation in low count-rate experiments: 85Kr β activity in the test facility of the Borexino detector and double-beta decay of 76Ge in the Heidelberg–Moscow experiment

Statistical methods for low count-rate experiments are reviewed and applied to two samples of experimental data. In one case the β activity of 85Kr in the test facility of the Borexino detector is determined. In another case a data sample from the Heidelberg–Moscow experiment used to claim the discovery of the neutrinoless double-beta decay of 76Ge is analyzed. Exploiting a Bayesian technique a conservative upper limit on the half-life of the 0ν2β decay of 76Ge is found at T1/20ν⩾1.2×1025 yr (90% CL) in the window (2000–2080) keV.