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Although statistical literacy has become a key competence in today's data-driven society, it is usually not a part of statistics education. To address this issue, we propose an innovative concept for a conference-like seminar on the topic of statistical literacy. This seminar draws attention to the relevance and importance of statistical literacy, and moreover, students are made aware of the process of science communication and are introduced to the peer review process for the assessment of scientific papers. In the summer term 2020, the seminar was conducted as a joint project by the University of Hamburg, the University of Muenster, and the Joachim Herz Foundation. In this article, we present the concept of the seminar and our experience with this concept in the summer term 2020.

Statistical modeling of epidemiological curves to capture the course of epidemic processes and to implement a signaling system for detecting significant changes in the process is a challenging task, especially when the process is affected by political measures. As previous monitoring approaches are subject to various problems, we develop a practical and flexible tool that is well suited for monitoring epidemic processes under political measures. This tool enables monitoring across different epochs using a single statistical model that constantly adapts to the underlying process, and therefore allows both retrospective and on‐line monitoring of epidemic processes. It is able to detect essential shifts and to identify anomaly conditions in the epidemic process, and it provides decision‐makers a reliable method for rapidly learning from trends in the epidemiological curves. Moreover, it is a tool to evaluate the effectivity of political measures and to detect the transition from pandemic to endemic. This research is based on a comprehensive COVID‐19 study on infection rates under political measures in line with the reporting of the Robert Koch Institute covering the entire period of the pandemic in Germany. [ABSTRACT FROM AUTHOR]

Mathematical data science combines mathematical techniques with data science methods to extract insights from data. It involves working with data at all stages of the data life cycle and using various tools and techniques to analyze data. This field is applied in business, industry, and medicine to make predictions, identify patterns, and draw conclusions from data. The special issue of Mathematics presents ten papers that showcase innovative mathematical data science techniques in solving complex problems across different domains. These papers cover topics such as modeling failure times, time series analysis, process capability indices, control charts, internet usage monitoring, and more. The authors emphasize the importance of integrating advanced mathematical techniques with emerging technologies to drive innovation in data science. [Extracted from the article]

This document is an editorial introducing a special issue of the journal "Symmetry" on the topic of symmetrical and asymmetrical distributions in statistics and data science. The editorial provides a summary of the contributions to the special issue, which include studies on topics such as control charts, copulas, statistical distributions, discretization methods, spatial dependence, queuing models, survival analysis, and reliability analysis. The authors invite researchers to submit contributions to a second volume of the special issue, with a potential focus on the hypergeometric and negative hypergeometric distributions. [Extracted from the article]

In this paper, an exponential autoregressive model for complex time series data is presented. As for estimating the parameters of this nonlinear model, a three-step procedure based on quantile methods is proposed. This quantile-based estimation technique has the benefit of being more robust compared to least/absolute squares. The performance of the introduced exponential autoregressive model is evaluated by means of four established goodness-of-fit criteria. The practical utility of the novel time series model is showcased through a comparative analysis involving simulation studies and real-world data illustrations. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear time series model is developed for the case when the underlying time series data are reported by L R fuzzy numbers. To this end, we present a three-stage nonparametric kernel-based estimation procedure for the center as well as the left and right spreads of the unknown nonlinear fuzzy smooth function. In each stage, the nonparametric Nadaraya–Watson estimator is used to evaluate the center and the spreads of the fuzzy smooth function. A hybrid algorithm is proposed to estimate the unknown optimal bandwidths and autoregressive order simultaneously. Various goodness-of-fit measures are utilized for performance assessment of the fuzzy nonlinear kernel-based time series model and for comparative analysis. The practical applicability and superiority of the novel approach in comparison with further fuzzy time series models are demonstrated via a simulation study and some real-life applications. [ABSTRACT FROM AUTHOR]

In this paper, we present a number‐between‐events (NBE) control chart for monitoring the fraction nonconforming in finite horizon production (FHP) processes and related specific performance measures. When monitoring fractions nonconforming in FHP processes, the common binomial p$p$‐chart has two crucial limitations: the underlying distributional assumptions are violated when dealing with low‐volume production and a scarce efficiency in the case of processes characterized by a low fraction nonconforming. Thus, an efficient monitoring of FHP processes requires the selection of the correct underlying statistical model: in this case, a distribution from the hypergeometric family of discrete statistical distributions. An efficient statistical monitoring of processes with low fractions nonconforming can be achieved by means of discrete time‐between‐events (TBE) control charts, which count the number of units up to the appearance of a fixed number of nonconforming units in the sample. Here, we present a discrete TBE‐chart, denoted as NBE‐chart, based on the negative hypergeometric distribution that meets numerous requirements of efficient monitoring of FHP processes. The proposed control chart can be conveniently used for both low‐volume and mass production in processes with frequent changeovers. [ABSTRACT FROM AUTHOR]

Nonparametric tests do not rely on data belonging to any particular parametric family of probability distributions, which makes them preferable in case of doubt about the underlying population. Although the two‐tailed sign test is likely the most common nonparametric test for location problems, practitioners face serious drawbacks, such as its lack of statistical power and its inapplicability when information regarding data and hypotheses is uncertain or imprecise. In this paper, we generalize the two‐tailed sign test by embedding fuzzy hypotheses caused by uncertainty/imprecision regarding linguistic statements on fractions of underlying quantiles. By achieving this objective, (1) crucial limitations of the common two‐tailed sign test are mitigated/overcome, (2) various further strengths are incorporated into the sign test (e.g., meeting the trade‐off between point‐ and interval‐valued hypotheses, facilitated formulation of fuzzy hypotheses, standardization of membership functions), and (3) shortcomings that often come along with fuzzy hypothesis testing are avoided (e.g., higher complexity, fuzzy test decision, possibilistic interpretation of test results). In addition, we conduct a comprehensive case study using a real data set on the psychosocial status during the COVID‐19 pandemic. The results of the case study clearly indicate that the generalized two‐tailed sign test is preferable to the two‐tailed sign test with point‐ or interval‐valued hypotheses. [ABSTRACT FROM AUTHOR]

The sign test is one of the most popular nonparametric tests for location problems and allows testing for any quantile of a population. However, the common sign test has serious drawbacks such as loss of information by considering solely signs of observations but not their magnitudes, various problems related to handling of ties in the data, and the lack of embedding uncertainty regarding the fraction of underlying quantile. To address these issues, we present an extended sign test based on fuzzy categories and fuzzy formulated hypotheses that improves the generality, versatility, and practicability of the common sign test. This generalized test procedure is neat in theory and practice and avoids disadvantages that are often associated with fuzzy tests (e.g., a considerably higher complexity of the underlying model, a fuzzy test decision, and a possibilistic instead of a probabilistic interpretation of test results). In addition, we perform a comprehensive case study on COVID‐19 in HIV‐infected individuals with a focus on human body temperature and related measurement problems. The results of the study clearly indicate that fuzzy categories and fuzzy hypotheses improve the performance of the sign test. [ABSTRACT FROM AUTHOR]

In this article, we propose the generalized one-tailed hypergeometric test with fuzzy hypotheses for both test methods: significance testing (by controlling the type I error) and hypothesis testing (by controlling both error types). With regard to the fuzzy set theory, this test is the generalization of the conventional hypergeometric test for a proportion and provides an additional gradual consideration of the indifference zone in compliance with expert opinion or user priorities. Further, a practical application for one of the most promising resulting test types (right-tailed hypothesis testing) is carried out in statistical quality control. In particular, single sampling plans for attributes are determined via an algorithm based on the Fibonacci sequence. In addition, a parametric sensitivity analysis of calculated sampling plans is carried out in relation to changes of the lot size, consumer's and producer's risks, as well as of specified target values of quality levels. Moreover, the impact of various shapes of membership functions (piecewise linear, convex, concave, and s-shaped) is investigated by comparing respective sampling plans. [ABSTRACT FROM AUTHOR]

This paper gives a detailed overview of the current state of research in relation to the use of state space models and the KALMAN-filter in the field of stochastic claims reserving. Most of these state space representations are matrix-based, which complicates their applications. Therefore, to facilitate the implementation of state space models in practice, we present a scalar state space model for cumulative payments, which is an extension of the well-known chain ladder (CL) method. The presented model is distribution-free, forms a basis for determining the entire unobservable lower and upper run-off triangles and can easily be applied in practice using the KALMAN-filter for prediction, filtering and smoothing of cumulative payments. In addition, the model provides an easy way to find outliers in the data and to determine outlier effects. Finally, an empirical comparison of the scalar state space model, promising prior state space models and some popular stochastic claims reserving methods is performed. [ABSTRACT FROM AUTHOR]

Often, the claims reserves exceed the available equity of non-life insurance companies and a change in the claims reserves by a small percentage has a large impact on the annual accounts. Therefore, it is of vital importance for any non-life insurer to handle claims reserving appropriately. Although claims data are time series data, the majority of the proposed (stochastic) claims reserving methods is not based on time series models. Among the time series models, state space models combined with Kalman filter learning algorithms have proven to be very advantageous as they provide high flexibility in modeling and an accurate detection of the temporal dynamics of a system. Against this backdrop, this paper aims to provide a comprehensive review of stochastic claims reserving methods that have been developed and analyzed in the context of state space representations. For this purpose, relevant articles are collected and categorized, and the contents are explained in detail and subjected to a conceptual comparison. [ABSTRACT FROM AUTHOR]

In stochastic claims reserving, state space models have been used for almost 40 years to forecast loss reserves and to compute their mean squared error of prediction. Although state space models and the associated Kalman filter learning algorithms are very powerful and flexible tools, comparatively few articles on this topic were published during this period. Most recently, several articles have been published which highlight the benefits of state space models in stochastic claims reserving and may lead to a significant increase in its popularity for applications in actuarial practice. To further emphasize the merits of these papers, this commentary highlights various additional aspects that are useful for practical applications and offer some fruitful directions for future research. [ABSTRACT FROM AUTHOR]

In machine learning, the fused lasso is a regularization technique that is used to handle problems where the underlying signal has some kind of structure. In this paper, we extend fused lasso estimation for regression models characterized by fuzzy predictors and fuzzy responses. We present the first fused lasso regression model that is able to handle and analyze high-dimensional fuzzy data. The proposed model provides feature selection, leads to an improved predictive performance, and ensures interpretable and explainable models, all while being computationally efficient. Moreover, it can recover the true signal more accurately, find solutions that are structurally sparse, and is robust to noise. We conduct comprehensive comparative analysis and demonstrate the practical applicability of the presented fuzzy regression model through simulation and real-life applications. [ABSTRACT FROM AUTHOR]

When dealing with nonparametric regression problems, kernel-based methods are often employed. In this paper, we investigate nonparametric regression problems with fuzzy responses and exact predictors by implementing an extended center and range method within a three-stage procedure. For this purpose, we utilize the Nadaraya–Watson estimator for estimating the unknown fuzzy smooth function. In each stage, the unknown bandwidth is determined with the help of a generalized cross validation criterion. To evaluate and to compare the performance of our proposed fuzzy nonparametric regression model with established regression models, different goodness-of-fit criteria are considered. Finally, we investigate the practical applicability and show the superiority of the proposed regression model by means of a simulation study and real data applications. • We develop a nonparametric regression model for fuzzy responses and exact predictors. • The nonlinear fuzzy smooth function is estimated within a three-stage procedure. • In each stage, the unknown bandwidth is evaluated by a generalized cross validation criterion. • We investigate different kernel functions and examine the model performance by various goodness-of-fit criteria. • We perform comparative analysis through simulation and real-life applications. [ABSTRACT FROM AUTHOR]