Bücher von Hung T. Nguyen

This is the first half of a text for a two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: Volume I, Probability for Statistics, for the first semester, and Volume II, Statistical Inference, for the second. We suggest that the following distinguish this text from other introductions to mathematical statistics. 1. The most obvious thing is the layout. We have designed each lesson for the (U.S.) 50 minute class; those who study independently probably need the traditional three hours for each lesson. Since we have more than (the U.S. again) 90 lessons, some choices have to be made. In the table of contents, we have used a * to designate those lessons which are "e;interesting but not essential"e; (INE) and may be omitted from a general course; some exercises and proofs in other lessons are also "e;INE"e;. We have made lessons of some material which other writers might stuff into appendices. Incorporating this freedom of choice has led to some redundancy, mostly in definitions, which may be beneficial.

This research monograph presents basic foundational aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Fuzzy data are modeled as observations from random fuzzy sets. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The monograph also aims at motivating statisticians to look at fuzzy statistics to enlarge the domain of applicability of statistics in general.Hung T. Nguyen is a professor of Mathematical Sciences at New Mexico State University, USA.Berlin Wu is a professor of Mathematical Sciences at National Chengchi University, Taipei, Taiwan.

if the measured value is 1.0, and inaccuracy is bounded by 0.1, then the actual (unknown) value of the quantity can be anywhere between 1.0 - 0.1 = 0.9 and 1.0 + 0.1 = 1.1.

It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision.

Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures.

But we know precious little about human reasoning processes, learning mechanisms and the like, and in particular about reasoning with limited, imprecise knowledge. In a sense, intelligent systems are machines which use the most general form of human knowledge together with human reasoning capability to reach decisions.

This is a text (divided into two volumes) for a two semester course in Mathematical Statistics at the Senior/Graduate level. Volume II: Statistical Inference is designed for the second semester and contains a rigorous introduction to Mathematical Statistics, from random samples to asymptotic theory of statistical inference.

This book presents basic aspects for a theory of statistics with fuzzy data, together with a set of practical applications. The book aims at motivating statisticians to examine fuzzy statistics to enlarge the domain of applicability of statistics in general.

It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision.

Points out gaps in the way data fusion problems are conceptually treated and addresses this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic way. This book offers research progress on data fusion and serves as an introduction to powerful techniques.

Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures.

But we know precious little about human reasoning processes, learning mechanisms and the like, and in particular about reasoning with limited, imprecise knowledge. In a sense, intelligent systems are machines which use the most general form of human knowledge together with human reasoning capability to reach decisions.