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Probabilistic modeling of random variables with inconsistent data

机译：具有不一致数据的随机变量的概率建模

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The aim of the present paper was to formulate probabilistic modeling for random variables with inconsistent data to facilitate accurate reliability assessment. Traditionally, random variables have some outputs available, based on which, some distribution is identified. However, as will be illustrated, the data relevant to those extreme events might not necessarily follow the same distribution as well as the other part, but they generally have small weights in the definition of the distribution due to their small quantity. The adoption of one single probabilistic distribution to describe random variables with such inconsistent data might cause great errors in the reliability assessment, especially for extreme events. One new formulation of probabilistic modeling is proposed here for such type of random variables. The inconsistency within the data set is identified and based on how the set is divided. Each division is described by the respective distribution and finally they are unified into one framework. The relevant problems in the modeling (e.g., the identification of the boundary between the divisions, the definition of the probability distributions, and the unification of the distributions into one framework) are presented and solved. The realization of the proposed approach in the practical numerical analysis is further investigated afterwards. Finally, two examples are presented to illustrate the application from different perspectives. (C) 2019 Elsevier Inc. All rights reserved.
机译：本文的目的是制定具有不一致数据的随机变量的概率模型，以促进准确的可靠性评估。传统上，随机变量具有一些可用的输出，基于该输出，识别出一些分布。然而，如将说明，与这些极端事件相关的数据可能不一定遵循相同的分布以及另一部分，但由于它们的少量，它们通常在分配的定义中具有小权重。采用一种单一的概率分布来描述具有此类不一致数据的随机变量可能会导致可靠性评估中的巨大错误，特别是对于极端事件。这里提出了一种新的概率建模的制剂，用于这种类型的随机变量。数据集中的不一致是识别的，并基于该组的划分方式。每个划分都是由相应的分布描述，最后它们统一到一个框架中。提出和解决了建模中的相关问题（例如，分割的边界，概率分布的定义以及分布到一个框架的统一）。之后进一步研究了在实际数值分析中实现了所提出的方法。最后，提出了两个示例以说明来自不同观点的应用。 （c）2019 Elsevier Inc.保留所有权利。

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