Development of a new general class of bivariate distributions based on reversed hazard rate order

IF 1.5 3区数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computational Statistics & Data Analysis Pub Date : 2024-11-26 DOI:10.1016/j.csda.2024.108106

Na Young Yoo , Hyunju Lee , Ji Hwan Cha

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Abstract

Motivated by real data sets to be analyzed in this paper, we develop a new general class of bivariate distributions that can model the effect of the so-called ‘load-sharing configuration’ in a system with two components based on the reversed hazard rate. Under such load-sharing configuration, after the failure of one component, the surviving component has to shoulder extra load, which eventually results in its failure at an earlier time than what is expected under the case of independence. In the developed class of bivariate distributions, it is assumed that the residual lifetime of the remaining component is shortened according to the reversed hazard rate order. We derive the joint survival function, joint probability density function and the marginal distributions. We discuss a bivariate ageing property of the developed class of distributions. Some specific families of bivariate distributions which can be usefully applied in practice are obtained. These families of bivariate distributions are applied to some real data sets to illustrate their usefulness.

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基于逆向风险率顺序的一类新的二元分布的发展

在本文要分析的真实数据集的激励下，我们开发了一种新的一般类型的二元分布，它可以基于反向风险率对具有两个组件的系统中所谓的“负载共享配置”的影响进行建模。在这种负载分担配置下，在一个组件失效后，幸存的组件必须承担额外的负载，最终导致该组件的失效时间比独立情况下的预期时间要早。在二元分布的发达类别中，假定剩余成分的剩余寿命按照颠倒的危险率顺序缩短。导出了联合生存函数、联合概率密度函数和边际分布。我们讨论了已发展的一类分布的二元老化性质。得到了一些可以在实际中应用的特殊的二元分布族。这些双变量分布族应用于一些实际数据集来说明它们的有用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Statistics & Data Analysis 数学-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

167

审稿时长

60 days

期刊介绍： Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]