Number Theoretic Methods In Statistics
Download Number Theoretic Methods In Statistics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Number Theoretic Methods In Statistics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Number-Theoretic Methods in Statistics
This book is a survey of recent work on the application of number theory in statistics. The essence of number-theoretic methods is to find a set of points that are universally scattered over an s-dimensional unit cube. In certain circumstances this set can be used instead of random numbers in the Monte Carlo method. The idea can also be applied to other problems such as in experimental design. This book will illustrate the idea of number-theoretic methods and their application in statistics. The emphasis is on applying the methods to practical problems so only part-proofs of theorems are given.
Number-theoretic Methods in Statistics
This book contains some of the research work conducted by the authors in past seventeen years. Our research started in 1976. At that time, the first author was studying a problem of alloy steel standardization, where aseries of probabilities of the 5-dimensional normal distribution needed to be calculated. Since the usual meth ods for numerical evaluation of multiple definite integral were all ineffective, he asked the second author for input on the number theoretic method for numerical integration. As a result, his prob lem was solved by using the number-theoretic method. The essence of the number-theoretic method (NTM) is to find a set of points that is uniformly scattered over an s-dimensional unit cube, and sometimes this set can be used instead of random number in Monte Carlo method. The authors then understood that this idea can apply also to some other problems, for instance, problems in ex perimental design. In 1978, a Chinese industrial agency proposed a problem of ex perimental designs to the authors, where six factors with at least 12 levels for each factors should be considered. Since the experiment was quite expensive, we were asked to provide an efficient exper imental design within 50 experiments. This lead us to study the problem on how to apply the number-theoretic method to arrange the experiments, and we proposed a so-called "uniform design" for designing experiments.
Numerical Methods of Statistics
Author: John F. Monahan
language: en
Publisher: Cambridge University Press
Release Date: 2001-02-05
This 2001 book provides a basic background in numerical analysis and its applications in statistics.