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

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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.