数理统计与应用：英文版 Tsokos & Ramachandran

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"Mathematical Statistics with Applications" 是一本由Chris P. Tsokos编写的数理统计学应用书籍，由Elsevier Academic Press在2009年出版。这本书专注于将数理统计理论应用于实际问题，旨在帮助读者理解并掌握统计学的基本概念和方法。书中的内容可能涵盖了广泛的统计学主题，包括概率论基础、抽样分布、估计理论、假设检验、线性回归分析、方差分析、时间序列分析以及非参数统计等。作者Kandethody M. Ramachandran和Chris P. Tsokos都是来自美国南佛罗里达大学数学与统计系的教授，他们的专业背景确保了教材的权威性和实用性。配合这本书的教学，Elsevier出版社提供了丰富的教学资源。教师可以访问http://textbooks.elsevier.com获取更多教学资料。此外，有一个配套网站http://www.elsevierdirect.com/companions/9780123748485，提供了与教材内容相辅相成的网络资源。这些资源可能包括精心挑选的补充网站链接，帮助学生扩展学习。对于学生，有在线学生解决方案手册可供购买，这是一个强大的学习工具，可以帮助他们解决教材中的练习题。而购买本书的教师还可以获得激活后受保护的在线教师解决方案手册，这将提供完整的习题解答，便于教学使用。此外，所有书中图表都以PowerPoint幻灯片和jpeg图像的形式提供，方便教师在课堂上使用。这样的多媒体资源使得教学更加生动，有助于提高学生对统计学的理解。 "Mathematical Statistics with Applications" 不仅是一本深入探讨数理统计原理的教科书，还是一套全面的教学工具包，旨在满足教师和学生在教学和学习过程中的各种需求。通过这本书，读者不仅可以学习到统计学的基本理论，还能掌握如何将这些理论应用于实际问题中，提升解决问题的能力。

Preface

This textbook is of an interdisciplinary nature and is designed for a two- or one-semester course in

probability and statistics, with basic calculus as a prerequisite. The book is primarily written to give

a sound theoretical introduction to statistics while emphasizing applications. If teaching statistics

is the main purpose of a two-semester course in probability and statistics, this textbook covers all

the probability concepts necessary for the theoretical development of statistics in two chapters, and

goes on to cover all major aspects of statistical theory in two semesters, instead of only a portion of

statistical concepts. What is more, using the optional section on computer examples at the end of

each chapter, the student can also simultaneously learn to utilize statistical software packages for data

analysis. It is our aim, without sacriﬁcing any rigor, to encourage students to apply the theoretical

concepts they have learned. There are many examples and exercises concerning diverse application

areas that will show the pertinence of statistical methodology to solving real-world problems. The

examples with statistical software and projects at the end of the chapters will provide good perspective

on the usefulness of statistical methods. To introduce the students to modern and increasingly popular

statistical methods, we have introduced separate chapters on Bayesian analysis and empirical methods.

One of the main aims of this book is to prepare advanced undergraduates and beginning graduate

students in the theory of statistics with emphasis on interdisciplinary applications. The audience for

this course is regular full-time students from mathematics, statistics, engineering, physical sciences,

business, social sciences, materials science, and so forth. Also, this textbook is suitable for people

who work in industry and in education as a reference book on introductory statistics for a good

theoretical foundation with clear indication of how to use statistical methods. Traditionally, one of

the main prerequisites for this course is a semester of the introduction to probability theory. A working

knowledge of elementary (descriptive) statistics is also a must. In schools where there is no statistics

major, imposing such a background, in addition to calculus sequence, is very difﬁcult. Most of the

present books available on this subject contain full one-semester material for probability and then,

based on those results, continue on to the topics in statistics. Also, some of these books include in their

subject matter only the theory of statistics, whereas others take the cookbook approach of covering

the mechanics. Thus, even with two full semesters of work, many basic and important concepts in

statistics are never covered. This book has been written to remedy this problem. We fuse together

both concepts in order for students to gain knowledge of the theory and at the same time develop

the expertise to use their knowledge in real-world situations.

Although statistics is a very applied subject, there is no denying that it is also a very abstract subject.

The purpose of this book is to present the subject matter in such a way that anyone with exposure

to basic calculus can study statistics without spending two semesters of background preparation.

To prepare students, we present an optional review of the elementary (descriptive) statistics in

Chapter 1. All the probability material required to learn statistics is covered in two chapters. Stu-

dents with a probability background can either review or skip the ﬁrst three chapters. It is also our

belief that any statistics course is not complete without exposure to computational techniques. At

xvi Preface

the end of each chapter, we give some examples of how to use Minitab, SPSS, and SAS to statistically

analyze data. Also, at the end of each chapter, there are projects that will enhance the knowledge and

understanding of the materials covered in that chapter. In the chapter on the empirical methods, we

present some of the modern computational and simulation techniques, such as bootstrap, jackknife,

and Markov chain Monte Carlo methods. The last chapter summarizes some of the steps necessary

to apply the material covered in the book to real-world problems. The ﬁrst eight chapters have been

class tested as a one-semester course for more than 3 years with ﬁve different professors teaching.

The audience was junior- and senior-level undergraduate students from many disciplines who had

had two semesters of calculus, most of them with no probability or statistics background. The feed-

back from the students and instructors was very positive. Recommendations from the instructors and

students were very useful in improving the style and content of the book.

AIM AND OBJECTIVE OF THE TEXTBOOK

This textbook provides a calculus-based coverage of statistics and introduces students to methods of

theoretical statistics and their applications. It assumes no prior knowledge of statistics or probability

theory, but does require calculus. Most books at this level are written with elaborate coverage of

probability. This requires teaching one semester of probability and then continuing with one or

two semesters of statistics. This creates a particular problem for non-statistics majors from various

disciplines who want to obtain a sound background in mathematical statistics and applications.

It is our aim to introduce basic concepts of statistics with sound theoretical explanations. Because

statistics is basically an interdisciplinary applied subject, we offer many applied examples and relevant

exercises from different areas. Knowledge of using computers for data analysis is desirable. We present

examples of solving statistical problems using Minitab, SPSS, and SAS.

FEATURES

■ During years of teaching, we observed that many students who do well in mathematics courses

ﬁnd it difﬁcult to understand the concept of statistics. To remedy this, we present most of

the material covered in the textbook with well-deﬁned step-by-step procedures to solve real

problems. This clearly helps the students to approach problem solving in statistics more

logically.

■ The usefulness of each statistical method introduced is illustrated by several relevant examples.

■ At the end of each section, we provide ample exercises that are a good mix of theory and

applications.

■ In each chapter, we give various projects for students to work on. These projects are designed

in such a way that students will start thinking about how to apply the results they learned in

the chapter as well as other issues they will need to know for practical situations.

■ At the end of the chapters, we include an optional section on computer methods with Minitab,

SPSS, and SAS examples with clear and simple commands that the student can use to analyze

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