TY - CHAP A1 - Schmiedt, Anja Bettina A1 - Neumaier, Stefanie T1 - "Gamification trifft Hybride Lehre" – Über ein Lehrprojekt in der mathematischen Statistik T2 - MINT Symposium 2023 - MINT-Lehre gemeinsam gestalten, Lehre erforschen, Wissen teilen N2 - Unter dem Titel „Gamification trifft Hybride Lehre“ wurde im Sommersemester 2023 ein Lehrprojekt im Fach Statistik des Studiengangs Wirtschaftsmathematik-Aktuarwissenschaften der Technischen Hochschule Rosenheim durchgeführt. Unterschiedliche hybrid-synchrone Lernsettings wurden in einem technisch entsprechend ausgestatteten Lehr-Experimentierraum mit den Studierenden erprobt. Als Ansatz zur Vor- und Nachbereitung der hybriden Lehre kam Gamification bzw. Gameful Motivation zum Einsatz. Im Lehrprojektteam mit Stefanie Neumaier wurde die hybride Lehre mittels der sog. EMPAMOS-Methode vorbereitet und reflektiert. Dabei ging es nicht darum, den spielfremden Kontext (die hybride Lehre) in ein Spiel zu verwandeln, sondern Spielelemente zur Zielerreichung einzusetzen. Die Auseinandersetzung mit hybriden Formaten wird dabei für Studierende und Lehrende als ein Zukunftsthema gesehen, nicht zuletzt für den Erwerb von Future Skills in einer Arbeitswelt, in der sich hybride Kollaboration etabliert. KW - Gamification KW - Hybride Lehre Y1 - 2023 SP - 159 EP - 166 ER - TY - JOUR A1 - Schmiedt, Anja Bettina A1 - Cramer, Erhard T1 - Generalized Ng–Kundu–Chan model of adaptive progressive Type-II censoring and related inference JF - Naval Research Logistics (NRL) N2 - The model of adaptive progressive Type-II censoring introduced by Ng et al. (2009) (referred to as Ng–Kundu–Chan model) is extended to allow switching from a given initial censoring plan to any arbitrary given plan of the same length. In this generalized model, the joint distribution of the failure times and the corresponding likelihood function is derived. It is illustrated that the computation of maximum likelihood and Bayesian estimates are along the same lines as for standard progressive Type-II censoring. However, the distributional properties of the estimators will usually be different since the censoring plan actually applied in the (generalized) Ng–Kundu–Chan model is random. As already mentioned in Cramer and Iliopoulos (2010), we directly show that the normalized spacings are independent and identically exponentially distributed. However, it turns out that the spacings themselves are generally dependent with mixtures of exponential distributions as marginals. These results are used to study linear estimators. Finally, we propose an algorithm for generating random numbers in the generalized Ng–Kundu–Chan model and present some simulation results. The results obtained also provide new findings in the original Ng–Kundu–Chan model; the corresponding implications are highlighted. KW - adaptive progressive censoring KW - exponential distribution KW - likelihood inference KW - linear inference KW - Ng–Kundu–Chan model KW - progressive Type-II censoring KW - spacings Y1 - 2024 U6 - https://doi.org/10.1002/nav.22152 VL - 71 IS - 3 SP - 389 EP - 415 ER - TY - JOUR A1 - Schmiedt, Anja Bettina A1 - Weiß, Christian T1 - The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms JF - Journal of Number Theory N2 - In any dimension d≥2, there is no known example of a low-discrepancy sequence which possesses Poisssonian pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have β-Poissonian pair correlations for all 0<β<1/d and are therefore arbitrarily close to having Poissonian pair correlations (which corresponds to the case β=1/d). In this paper, we further elaborate on the closeness of the two notions. We show that d-dimensional Kronecker sequences for badly approximable vectors α→ with an arbitrary small uniformly distributed stochastic error term generically have β=1/d-Poissonian pair correlations. KW - Kronecker sequences KW - Poissonian pair correlations KW - Uniform distribution Y1 - 2024 U6 - https://doi.org/10.1016/j.jnt.2023.12.011 VL - 259 SP - 422 EP - 437 ER -