Date/Time Date(s) - 25/09/20251:30 pm - 2:30 pm
Speaker: Dr. Erhard Cramer (RWTH Aachen University)
Location: Hamilton Hall, Room 102
Title: Modularization of hybrid censoring schemes, with applications to minimal repair and record data
Abstract: Recently, Berzborn, Cramer (2024) applied hybrid censoring schemes to minimal repair and record data using the idea of samples with replacement proposed in Epstein (1954). In particular, they utilized the refined modularization/decomposition approach to conduct statistical inference (see Cramer (2025), Górny, Cramer (2018)). The resulting decomposition can be used to derive the exact (conditional) distribution of the MLE for exponentially distributed lifetimes and leads to compact expressions of the MLE’s density function in terms of gamma distributions. Furthermore, it turns out that the distributions have point masses at infinitely many points. A general design approach for hybrid censoring schemes has recently been presented in van Bentum, Cramer (2025) illustrating that the method can be applied to any hybrid censoring scheme designed in a specific way. For a recent review on hybrid censoring, we refer to the monograph Balakrishnan et al. (2023).
The presentation provides an introduction to both hybrid censoring and the modularization approch. In particular, applications to likelihood inference, prediction, and statistical intervals are presented for minimal repair data/record data.