Statistical control charts have found valuable applications in health care, having been largely adopted from operations research in manufacturing. However, the most common types are not best-suited ...to monitor high-yield processes (outcomes comprising true/false fractions, ‘near-zero’) and periodical processes (characterized by sequences of single populations of finite sizes), but rather to monitor variable vital signs levels and, to a lesser degree, service performance indicators. We discuss control charts that are most suitable for fraction non-conforming measurements. We focus particularly on high-yield and periodical processes, i.e. range in which out-of-control conditions are expected and should be identified. For these conditions, we discuss control charts based on the family of hypergeometric distributions, explaining and comparing their application to more traditional alternatives with two health care case studies. We demonstrate that hypergeometric-type control charts provide higher sensitivity in timely identification of changing rare event fractions and are well-suited for monitoring of periodical processes, while remaining more resistant to false alarms, versus their alternatives.
This paper is concerned with fuzzy hypothesis testing in the framework of the randomized and non-randomized hypergeometric test for a proportion. Moreover, we differentiate between a test of ...significance and an alternative test to control the type I error or both error types simultaneously. In contrast to classical (non-)randomized hypothesis testing, fuzzy hypothesis testing provides an additional gradual consideration of the indifference zone in compliance with expert opinion or user priorities. In particular, various types of hypotheses with user-specified membership functions can be formulated. Additionally, the proposed test methods are compared via a comprehensive case study, which demonstrates the high flexibility of fuzzy hypothesis testing in practical applications.
•Comprehensive literature review of statistical and intelligent models to predict firms failure•Investigation of the discriminatory power of a Multilayer Perceptron for bankruptcy ...prediction•Consideration of numerous parameter setups and various evaluation metrics•Extensive case study including comparative analysis based on a data set of Taiwanese firms•Critical examination of methodologies and discrepancies in the results
High bankruptcy rates can lead to the collapse of economic systems. Therefore, having accurate and reliable models to predict firms in financial distress allows for proper management of the economic losses helping to prevent such crises. Since the 1930s, more than 500 studies have been published in the field of bankruptcy prediction models. In this paper, we firstly give a comprehensive literature review on the topic of statistical and intelligent models to predict firms failure. Then, we closely examine the discriminatory power of a Multilayer Perceptron (MLP) in the context of bankruptcy prediction. For this purpose, we consider different setups of optimization algorithms, activation functions, number of neurons, and number of layers. To find the parameter setup that achieves the best results, we use various evaluation metrics such as average accuracy, specificity, sensitivity, and precision. The case study is based on a data set of Taiwanese firms and includes comprehensive comparative analysis. The proposed MLPs show superior performance, and we critically examine the differences between the methodologies to explain the discrepancies in the results.
This paper delves into the theoretical and practical exploration of the complementary Bell Weibull (CBellW) model, which serves as an analogous counterpart to the complementary Poisson Weibull model. ...The study encompasses a comprehensive examination of various statistical properties of the CBellW model. Real data applications are carried out in three different fields, namely the medical, industrial and actuarial fields, to show the practical versatility of the CBellW model. For the medical data segment, the study utilizes four data sets, including information on daily confirmed COVID-19 cases and cancer data. Additionally, a Group Acceptance Sampling Plan (GASP) is designed by using the median as quality parameter. Furthermore, some actuarial risk measures for the CBellW model are obtained along with a numerical illustration of the Value at Risk and the Expected Shortfall. The research is substantiated by a comprehensive numerical analysis, model comparisons, and graphical illustrations that complement the theoretical foundation.
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.
In this article, we discuss a new extension of the Rayleigh-Weibull model using the Marshall-Olkin family of distributions. The proposed model is called the Marshall-Olkin-Rayleigh-Weibull (MORW) ...model. Various statistical properties of the MORW distribution are discussed, including explicit expressions for quantiles, moments, incomplete and conditional moments, some inequality measures, moment generating function, moments of the residual and reversed residual life, the Rényi entropy, and order statistics. Six different estimation methods are considered to investigate the behavior of the model parameters within the MORW model. A Monte Carlo simulation study is conducted to evaluate the performance of these different estimators. In addition, some actuarial measures, such as the Value-at-Risk, the expected shortfall, the tail Value-at-Risk, the tail variance, the tail variance premium, the tail conditional expectation, and the tail standard deviation premium, are calculated. Finally, applying the model to real data sets illustrates the applicability and usefulness of the MORW distribution.
Machine learning applied to regression models offers powerful mathematical tools for predicting responses based on one or more predictor variables. This paper extends the concept of multiple linear ...regression by implementing a learning system and incorporating both fuzzy predictors and fuzzy responses. To estimate the unknown parameters of this soft regression model, the approach involves minimizing the absolute distance between two lines under three constraints related to the absolute error distance between observed data and their respective predicted lines. A thorough comparative analysis is conducted, showcasing the practical applicability and superiority of the proposed soft multiple linear regression model. The effectiveness of the model is demonstrated through a comprehensive examination involving simulation studies and real-life application examples.
•Developing a machine learning-based regression model with fuzzy predictors and fuzzy responses.•Providing a framework for reducing prediction errors and mitigating their impact on the predictions.•Allowing for higher flexibility in handling a wide range of data types and structures.•Enabling the incorporation of partial or incomplete information.•Investigating the practical applicability in the context of four application examples.
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.
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