U.S.-Egypt Cooperative Research: Informational and Statistical Research Topics on Aging

0421124艾哈迈德描述：该奖项旨在支持佛罗里达州奥兰多市中佛罗里达大学统计学系Ibrahim Ahmad博士与埃及开罗大学统计研究与研究所数理统计与运筹学系Hady Ahmed博士之间的合作研究。在生命检验中，有三个概念主导着它的发展，它们是随机生命本身，特定时间t的随机剩余生命和平衡或平稳随机生命。基于这些随机变量的各种类型的随机比较，描述生命衰变的生命分布的类别已经在文献中被介绍和研究了几十年。过去发展的概念，如危险率和平均剩余寿命，已被证明在许多领域有用，包括医学、生物统计学、可靠性和质量以及保险。pi将研究法医学（死亡后的时间）、老年医学（研究老年）、失败后的时间（生产线）等不同领域中重要的新概念。这些新概念包括“反向危险率”和“平均不活动时间”。在此基础上，pi将定义新的课程，从新的角度解决生活问题。pi将把这种方法应用于基本可靠性和寿命测试函数之间的相互关系，所有这些都将根据随机比较来定义。这项研究统一了对老年家庭生活分布的处理，使其更容易将大量此类类别彼此联系起来，并清楚地定义遏制属性。它还有助于将新形成的类定义为与已知类相关的物理解释，并使通过测试和估计对老化分布的类进行统计推断变得更加容易。范围和广泛影响：该项目将开发用于寿命估计的新概念的概率属性以及基于它们定义的类。它将提供这些类别的特征，冲击模型类别的形成及其推断（估计和假设检验）。统一的方法为寿命分布的老化类别的一些定义提供了实用价值（统计和物理），并开发了这些类别的新的统计和概率性质。这将为通过新技术进行生命测试多变量分布的研究打开大门。该方法有望在可靠性和寿命试验的许多领域引起新的研究兴趣。在推论部分，该项目将讨论通常用于生命数据研究的不同采样方案的案例，如审查、截断、微阵列数据和面板数据等。该项目得到了美国-埃及联合基金项目的支持，该项目向两国的科学家和工程师提供赠款，以开展这些合作活动。

0421124AhmadDescription: This award is to support a cooperative research between Dr. Ibrahim Ahmad, Department of Statistics, University of Central Florida, Orlando, Florida and Dr. Hady Ahmed, Department of Mathematical Statistics and Operations Research, Institute of Statistical Studies and Research, Cairo University, Cairo, Egypt. In life testing three notions dominate its development, these are the random life itself, the random residual life at a specific time t and the equilibrium or stationary random life. Based on various types of stochastic comparisons of these random variables, classes of life distributions that characterize decay in life have been introduced and studied in the literature for several decades now. Past-developed notions, such as the Hazard Rate and the Mean Residual Life, have proven useful in many areas including medicine, biostatistics, reliability and quality and insurance. The PIs will study new notions that are important in different studies as Forensic science (time since death), Geriatrics (studying old age), Times since Failure (in production lines). These new notions include the "Reversed hazard rate" and the "Mean inactivity time". From these the PIs will define new classes that address life from new angles. The PIs will apply this approach to the interrelations between basic reliability and life testing functions, all to be defined in terms of stochastic comparison. The research unifies the treatment of ageing families of life distributions, makes it easier to relate a large number of such classes to one another and define containment properties clearly. It also helps in defining physical interpretations of newly formed classes as related to already known ones, and makes it much easier to proceed with the statistical inference of classes of ageing distributions via testing and estimation. Scope and broad impact: This project will develop probabilistic properties of new notions for life estimation and the classes defined based on them. It will provide characterizations of these classes, formation of shock model classes and their inference (estimation and hypotheses testing). The unifying approach gives practical values (statistical and physical) to some definitions of ageing classes of life distributions, and develops new statistical and probabilistic properties of such classes. This should open the door for research in life testing multivariate distributions via the new technology. The method is hoped to renew research interest in many areas in reliability and life testing. In the inferential parts the project will address cases of different sampling schemes usually usable in the studies of life data such as censoring, truncation, micro-array data, and panel data among others. This project is being supported under the US-Egypt Joint Fund Program, which provides grants to scientists and engineers in both countries to carry out these cooperative activities.