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

0421124 Ahmad描述：该奖项是为了支持佛罗里达奥兰多中央佛罗里达大学统计系的Ibrahim Ahmad博士和埃及开罗开罗大学统计研究所数理统计和运筹学系的Hady Ahmed博士之间的合作研究。 在寿命试验中，三个概念支配着寿命试验的发展，它们是随机寿命本身、在特定时间t的随机剩余寿命和平衡或平稳随机寿命。 基于这些随机变量的各种类型的随机比较，描述寿命衰减的寿命分布类已经在文献中引入和研究了几十年。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，包括医学，生物统计学，可靠性和质量和保险有用。 PI将研究在不同研究中重要的新概念，如法医学（死亡时间），老年医学（研究老年），失败时间（生产线）。这些新概念包括“反向危险率”和“平均不活动时间”。从中，PI将定义从新角度解决生活问题的新类别。 PI将把这种方法应用于基本可靠性和寿命测试功能之间的相互关系，所有这些都将根据随机比较来定义。 该研究统一了对老龄化生命分布族的处理，使大量此类类彼此之间的关系更容易，并清楚地定义了包容性。它还有助于定义与已知类别相关的新形成类别的物理解释，并通过测试和估计更容易进行老化分布类别的统计推断。 范围和广泛的影响：该项目将开发新概念的概率特性，用于寿命估计和基于它们定义的类别。 它将提供这些类的特征，冲击模型类的形成及其推断（估计和假设检验）。 统一的方法给出了实用价值（统计和物理）的一些定义的老化类的寿命分布，并开发新的统计和概率性质的类。这将为通过新技术进行寿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重新引起人们的研究兴趣。 在推理部分，该项目将解决不同的抽样方案的情况下，通常可用于生命数据的研究，如删失，截断，微阵列数据，面板数据等。 该项目得到了美国-埃及联合基金方案的支持，该方案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.