Bivariate tempered space-fractional Poisson process and shock models

IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
Ritik Soni, Ashok Kumar Pathak, Antonio Di Crescenzo, Alessandra Meoli
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引用次数: 0

Abstract

We introduce a bivariate tempered space-fractional Poisson process (BTSFPP) by time-changing the bivariate Poisson process with an independent tempered $\alpha$ -stable subordinator. We study its distributional properties and its connection to differential equations. The Lévy measure for the BTSFPP is also derived. A bivariate competing risks and shock model based on the BTSFPP for predicting the failure times of items that undergo two random shocks is also explored. The system is supposed to break when the sum of two types of shock reaches a certain random threshold. Various results related to reliability, such as reliability function, hazard rates, failure density, and the probability that failure occurs due to a certain type of shock, are studied. We show that for a general Lévy subordinator, the failure time of the system is exponentially distributed with mean depending on the Laplace exponent of the Lévy subordinator when the threshold has a geometric distribution. Some special cases and several typical examples are also demonstrated.
双变量节制空间分数泊松过程和冲击模型
我们引入了双变量有节制空间分数泊松过程(BTSFPP),即用独立的有节制 $\alpha$ - 稳定从量对双变量泊松过程进行时变。我们研究了它的分布特性及其与微分方程的联系。我们还推导出了 BTSFPP 的 Lévy 度量。我们还探讨了一个基于 BTSFPP 的双变量竞争风险和冲击模型,用于预测经历两次随机冲击的物品的失效时间。当两种冲击的总和达到某个随机阈值时,系统就会崩溃。我们研究了与可靠性有关的各种结果,如可靠性函数、危险率、失效密度和因某类冲击而发生失效的概率。我们证明,对于一般的莱维从属器,当阈值具有几何分布时,系统的失效时间呈指数分布,其均值取决于莱维从属器的拉普拉斯指数。我们还展示了一些特例和几个典型例子。
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来源期刊
Journal of Applied Probability
Journal of Applied Probability 数学-统计学与概率论
CiteScore
1.50
自引率
10.00%
发文量
92
审稿时长
6-12 weeks
期刊介绍: Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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