Mathematical Methods of Probability and Statistics

Resonance ◽  
2016 ◽  
pp. 383-390
2017 ◽  
Vol 28 (2) ◽  
pp. 171
Author(s):  
John Robinson ◽  
Alan H. Welsh

Peter Hall, in the forty years of his research career, produced work in both probability and statistics, whose breadth and depth must be regarded as phenomenal. He displayed extraordinary technical skills together with remarkable intuition in developing and applying multifaceted mathematical approaches in the whole of his work. The impact of this wide-ranging use of powerful mathematical methods has had a profound effect on much of modern mathematical statistics. After completing his DPhil at Oxford, he remained in Australia for almost all his career although he was renowned as one of the major international figures in probability and statistics. Peter was a mentor to a large group of post-graduate students and post-doctoral colleagues giving encouragement and guidance and he attracted many research visitors contributing greatly to the whole of Australian statistical research. Remarkably, given his immense research output, he took a significant role in both editorial duties in major international journals and in advocacy for mathematics and statistics in Australia. Peter was a man of great charm whose modest demeanour belied his staggering abilities. His loss to mathematics and statistics is great, but is matched by the personal loss to us and to his many friends.


2018 ◽  
Vol 64 ◽  
pp. 207-229
Author(s):  
John Robinson ◽  
Alan H. Welsh

In the 40 years of his research career, Peter Hall produced work in both probability and statistics, the breadth and depth of which must be regarded as phenomenal. He displayed extraordinary technical skills together with remarkable intuition in developing and applying multifaceted mathematical approaches in the whole of his work. The impact of this wide-ranging use of powerful mathematical methods has had a profound effect on much of modern mathematical statistics. After completing his DPhil at Oxford, he remained in Australia for almost all of his career although he was renowned as one of the major international figures in probability and statistics. Peter was a mentor to a large group of postgraduate students and post-doctoral colleagues, giving encouragement and guidance, and he attracted many research visitors, contributing greatly to the whole of Australian statistical research. Remarkably, given his immense research output, he took a significant role both in editorial duties in major international journals and in advocacy for mathematics and statistics in Australia. Peter was a man of great charm whose modest demeanour belied his staggering abilities. His loss to mathematics and statistics is great, but is matched by the personal loss to us and to his many friends.


2017 ◽  
Vol 28 (2) ◽  
pp. 202
Author(s):  
John Robinson ◽  
Alan H. Welsh

Peter Hall, in the forty years of his research career, produced work in both probability and statistics, whose breadth and depth must be regarded as phenomenal. He displayed extraordinary technical skills together with remarkable intuition in developing and applying multifaceted mathematical approaches in the whole of his work. The impact of this wide-ranging use of powerful mathematical methods has had a profound effect on much of modern mathematical statistics. After completing his DPhil at Oxford, he remained in Australia for almost all his career although he was renowned as one of the major international figures in probability and statistics. Peter was a mentor to a large group of post-graduate students and post-doctoral colleagues giving encouragement and guidance and he attracted many research visitors contributing greatly to the whole of Australian statistical research. Remarkably, given his immense research output, he took a significant role in both editorial duties in major international journals and in advocacy for mathematics and statistics in Australia. Peter was a man of great charm whose modest demeanour belied his staggering abilities. His loss to mathematics and statistics is great, but is matched by the personal loss to us and to his many friends.


2018 ◽  
Vol 216 ◽  
pp. 02004 ◽  
Author(s):  
Grigory Gefan

Complex economic and mathematical methods are becoming more widespread in training of specialists in the field of railroad communication arrangement. The purpose of this study is to develop an effective methodology for mathematical training of railway transportation specialists on the basis of active training methods. The article deals with application of probabilistic and statistical methods to problems in design of railway transportation, for example, fluctuations in loading of railway stations and distribution of the time interval between arrival of trains. Using the example of the flow of arriving trains, the technology of testing the hypothesis that the time between arrival of trains is distributed according to the exponential law and the hypothesis of independence of events in the flow is displayed in detail. When confirming each of these hypotheses, it must be concluded that the flow of trains arriving at the station is according to the simplest (Poisson’s) model. This conclusion allows using the apparatus of Markov chains to describe a random process.


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