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    <title language="eng">Generalized Ng–Kundu–Chan model of adaptive progressive Type‐II censoring and related inference</title>
    <abstract language="eng">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.</abstract>
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(2009) (referred to as Ng\u2013Kundu\u2013Chan 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\u2010II censoring. However, the distributional properties of the estimators will usually be different since the censoring plan actually applied in the (generalized) Ng\u2013Kundu\u2013Chan 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. 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    <author>Anja Bettina Schmiedt</author>
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    <title language="deu">Über die strukturierte Entwicklung digitaler Lehr- und Lernformate mit EMPAMOS – Erkenntnisse aus einem Lehrprojekt</title>
    <abstract language="deu">Der vorliegende Beitrag diskutiert ausgewählte Schlaglichter eines hybriden Lehr- und Lernprojektes, welches mithilfe von EMPAMOS als Analyse-, Gestaltungs- und Reflexionsinstrument entwickelt und begleitet wurde. Das Lehrprojekt verfolgte das Ziel, hybride und digitale Lehre in einem Kurs zur mathematischen Statistik durch Gamification motivational ansprechend zu gestalten. Hierfür wurde das hybride Lehr- und Lernlabor als ein veränderliches Spielfeld verstanden, mit welchem es umzugehen galt, um stets handlungsfähig zu bleiben und Studierende adäquat auf das Bestehen des Leistungsnachweises vorzubereiten. Dabei konnte die kooperative Spielform als ein zentrales Spielelement identifiziert werden, mit dem sich dieser Auftrag umsetzen ließ. Bei den Studierenden hatte jedoch das immanente motivationale Bedürfnis nach Kompetenzerleben die höchste Priorität.</abstract>
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    <title language="eng">A flexible model of ordered random variables for non-metallic inclusions in steels and related statistical inference</title>
    <abstract language="eng">In a data set of non-metallic inclusion sizes in samples from engineering steel, common order statistics fail to serve as a suitable model for ascendingly ordered measurements within single samples. Therefore, a flexible model of ordered random variables is proposed, which allows for changes of distributions described by model parameters. Joint maximum likelihood estimation of these parameters and the shape parameter of an underlying left-truncated Weibull distribution is considered, and a model test is developed for the null-hypothesis of common order statistics being an adequate model. To overcome small data situations, a link-function approach is examined in order to reduce the number of involved model parameters as well as to propose to use a link-function parameter as a material indicator. An asymptotic test is provided to check for the presence of a linear link function, and tests for hypotheses about two link-function parameters are studied. Moreover, the construction of simultaneous confidence regions for the link-function parameters as well as of confidence bands for the entire graph of the link function are presented. Throughout, the findings are applied to the real metallurgical data set. Similar problems and data structures arise in other fields of material science and applications such as geology.</abstract>
    <parentTitle language="eng">Applied Mathematical Modelling</parentTitle>
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    <identifier type="doi">10.1016/j.apm.2025.116284</identifier>
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    <title language="eng">Prediction intervals for future Pareto record claims</title>
    <abstract language="eng">Stochastic models and methods for quantifying extreme events are of interest in numerous disciplines. Within this paper, statistical prediction of extreme claims or losses in insurance industry is considered based on upper record values, which describe successively largest observations in a sequence of data over time. The problem of predicting a future record value (here in particular, a future record claim) based on a sequence of previously observed record values (here, past record claims) is addressed by means of prediction intervals. For an underlying Pareto distribution, respective exact and approximate intervals from the literature are summarized and modified and new ones are developed. In a simulation study, these prediction intervals are evaluated and compared regarding coverage frequency and length. The impact of the number of observed record values as well as the choice of the Pareto distribution is discussed. In the case of a small number of record values, the use of k-th record values is considered as an option for statistical analyses to predict, e.g., second largest record claims. Selected prediction methods are applied to several real data sets, which turn out to perform well and to be able to capture the magnitude of future record claims, even for fairly small numbers of record observations. For comparison, generalized Pareto distributions are fitted to real data sets and a corresponding point predictor as well as a respective upper prediction interval for the next record to appear are derived and evaluated.</abstract>
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