Mathematical Sciences: Multi-Dimensional Statistical Analysis

DMS 9626265 Olkin本研究涉及从模型选择的角度研究寿命分布。其中一个阶段涉及生成族中的参数的方法。给定一个具有分布和生存函数的随机变量，有许多方法可以施加参数，在某些情况下，通过取随机变量的函数，在某些情况下，通过取分布函数或生存函数。下面是一些例子：(1)位置和尺度参数；(2)脆弱性和弹性参数；(3)功率参数；(4)卷积参数(用于特殊家庭，如伽马族)；(5)几何-极稳定参数。研究人员研究了这些参数族的序关系。例如，哪些参数族的风险函数是有序的；哪些族是随机或凸序的。参数及其特征和排序的介绍是深入了解如何将结果扩展到多变量分布的基础。虽然正态分布在许多应用和统计理论中发挥着核心作用，但它不能作为制造数据、材料数据、可靠性数据等工业应用中出现的寿命数据的模型，也不能作为健康或环境科学中的生存分析或风险分析的模型。这项研究集中在如何生成非正态参数族，以提供对此类数据的行为模式和预测的洞察。特别是，正在开发的方法用于提升工程应用中的风险和可靠性分析。这项研究的第二阶段是开发考虑到测量之间的相关性的多变量版本。

DMS 9626265 Olkin This research involves the study of life distributions from the point of view of model selection. One phase involves methods for generating parameters in families. Given a random variable with distribution and survival functions, there are a number of ways to impose parameters, in some instances by taking a function of the random variable, and in some cases by taking a function of the distribution or survival function. The following are some examples: (1) Location and scale parameters; (2) Frailty and resilience parameters; (3) Power parameter; (4) Convolution parameter (for special families such as the gamma family); (5) Geometric-extreme stable parameter. The investigators study order relations for these parametric families. For example, for which parametric families are the hazard functions ordered; for which families is there a stochastic or convex ordering. The introduction of parameters and their characteristics and their orderings is fundamental to an insight concerning how to extend the results to multivariate distributions. Although the normal distribution plays a central role in many applications and in statistical theory, it does not serve as a model for lifetime data arising in industrial applications such as manufacturing data, materials data, reliability data, nor does it serve as a model for survival analysis or risk analysis in the health or environmental sciences. This research focuses on how to generate non-normal parametric families that will provide an insight into behavior patterns and prediction for such data. In particular, the methods being developed serve to upgrade risk and reliability analyses in engineering applications. A second stage in this research is the development of multivariate versions that take account of dependencies among measurements.