Advanced in distribution theory with applications to transportation logistics and statistical genetics

我计划开发半参数方法密度估计，这是完全基于样本矩和研究相关的收敛问题。最近提出的微分对数密度近似值具有许多理想的性质，需要进一步研究。我将把我关于矩形和平行六面体中随机点之间距离分布的结果扩展到多边形和多边形金字塔中的随机点，并考虑运输物流的某些应用，例如与城市和城际交通相关的应用。广义分布的进一步发展将导致可靠性分析和质量控制方面更有效的技术。贝叶斯预测方法将用于对生物医学领域中出现的问题进行推断，特别是在统计遗传学中。与组件串联或并联连接的系统寿命相关的预测推理问题也将被研究。将已发表的时间序列分布结果推广到一般ARMA模型的研究也在进行中。我打算探索椭圆轮廓分布的另一种结构表示；使用厚尾分布式创新技术对时间序列进行建模，以及开发有效的替代技术来模拟涉及椭圆轮廓向量的函数，这些都是有前景的应用。我将利用某种符号计算软件包，开发一种确定不定二次型分布函数的简化而有效的算法；二次型在统计学中无处不在，应用非常广泛。最后，我的目标是完成一本关于多元统计分析的教科书，增加分类、多元方差分析和广义线性模型的章节。我也在准备一本关于密度估计的专著。

I am planning to develop semi-parametric approaches to density estimation, which are solely based on sample moments and to study related convergence issues. A recently proposed differentiated logdensity approximant, which turns out to possess numerous desirable properties, requires further investigation. I shall extend my results on the distribution of the distance between random points located in rectangles and parallelepipeds to random points located in polygons and polygonal pyramids, and consider certain applications to transportation logistics, such as those associated with urban and intercity traffic. Further developments on generalized distributions should lead to more efficient techniques in reliability analysis and quality control. The Bayesian predictive approach will be used to make inferences in connection with problems arising in the biomedical fields, and in particular, in statistical genetics. Predictive inference problems related to the life times of systems whose components are connected in series or in parallel will be also be studied. Extensions of the published distributional results in Time Series to general ARMA models are also being investigated. I intend to explore an alternative structural representation of elliptically contoured distributions; the modelling of time series with thick-tailed distributed innovations as well as the development of efficient alternative techniques for simulating functions involving elliptically contoured vectors constitute promising applications among others. I shall develop a simplified and efficient algorithm for determining the distribution function of indefinite quadratic forms by making use of a certain symbolic computational software package; quadratic forms being ubiquitous in Statistics, the applications are legion. Finally, I am aiming to complete a textbook on multivariate statistical analysis with the addition of chapters on classification, multivariate analysis of variance and generalized linear models. I am also preparing a monograph on the topic of density estimation.