数理统计学导论(英文版第7版)

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    数学书籍
《数理统计学导论(英文版第7版)》是数理统计方面的一本经典教材，自1959年出版以来，广受读者好评，并被众多院校选为教材，如布朗大学、乔治华盛顿大学等。
第7版延续了前几版的一贯风格，清晰而全面地阐述了数理统计的基本理论，并且为了让读者更好地理解数理统计，还提供了丰富的例子和一些重要的背景材料。与前几版相比，本版引入了最近新的数理统计发展成果，采用现在流行的R软件进行统计计算和推断。
《数理统计学导论(英文版第7版)》特色
全面覆盖估计和检验中的经典统计推断过程。
深入讨论充分性和检验理论，包括一致最大功效检验和似然比检验。
提供丰富的实例和练习，便于读者理解和巩固相关知识。
附录B中给出更多的R函数实例，帮助读者了解使用R进行统计计算与模拟。

　　Robert V. Hogg 是艾奥瓦大学统计与精算科学系教授，自1948年开始任教于艾奥瓦大学，在此从事教学和管理工作50多年，并帮助筹建了统计与精算科学系。曾担任美国统计协会（ASA）主席，并曾获得多项教学奖，包括美国数学协会杰出教育奖、Governor's Science Medal for Teaching。
　　Joseph W. McKean 西密西根大学统计系教授，ASA会士。他在线性、非线性、混合模型的稳健非参数处理方面已发表多篇论文，主要讲授统计学、概率论、统计方法、非参数理论等课程。
　　Allen T. Craig 艾奥瓦大学教授。

《数理统计学导论(英文版第7版)》
Preface
1 Probability and Distributions
1.1 Introduction
1.2 Set Theory
1.3 The Probability Set 'Function
1.4 Conditional Probability and Independence
1.5 Random Variables
1.6 Discrete Random Variables
1.6.1 Transformations
1.7 Continuous Random Variables
1.7.1 Transformations
1.8 Expectation of a Random Variable
1.9 Some Special Expectations
1.10 Important Inequalities
2 Multivariate Distributions
2.1 Distributions of Two Random Variables
2.1.1 Expectation
2.2 Transformations: Bivariate Random Variables
2.3 Conditional Distributions and Expectations

　　Changes for Seventh Edition
　　In the preparation of this seventh edition, our goal has remained steadfast: to produce an outstanding text in mathematical statistics. In this new edition, we have added examples and exercises to help clarify the exposition. For the same reason, we have moved some material forward. For example, we moved the discussion on some properties of linear combinations of random variables from Chapter 4 to Chapter 2. This helps in the discussion of statistical properties in Chapter 3 as well as in the new Chapter 4.
　　One of the major changes was moving the chapter on "Some Elementary Statistical Inferences," from Chapter 5 to Chapter 4. This chapter on inference covers confidence intervals and statistical tests of hypotheses, two of the most important concepts in statistical inference. We begin Chapter 4 with a discussion of a random.sample and point estimation. We introduce point estimation via a brief discussion of maximum likelihood estimation (the theory of maximum likelihood inference is still fullly discussed in Chapter 6). In Chapter 4, though, the discussion is illustrated with examples. After discussing point estimation in Chapter 4, we proceed onto confidence intervals and hypotheses testing. Inference for the basic one- and two-sample problems (large and small samples) is presented. We illustrate this discussion with plenty of examples, several of which are concerned with real data.We have also added exercises dealing with real data. The discussion has also been updated; for example, exact confidence intervals for the parameters of discrete distributions and bootstrap confidence intervals and tests of hypotheses are discussed,both of which are being used more and more in practice. These changes enable a one-semester course to cover basic statistical theory with applications. Such a course would cover Chapters 1-4 and, depending on time, parts of Chapter 5. For two-semester courses, this basic understanding of statistical inference will prove quite helpful to students in the later chapters (6-8) on the statistical theory of inference.
　　Another major change is moving the discussion of robustness concepts (influence function and breakdown) of Chapter 12 tO the end of Chapter 10. To reflect this move, the title of Chapter 10 has been changed to "Nonparametric and Robust Statistics." This additional material in the new Chapter 10 is essentially the important robustness concepts found in the old Chapter 12. Further, the simple linear model is discussed in Chapters 9 and 10. Hence, with this move we have eliminated Chapter 12.
　　Additional examples of R functions are in Appendix B to help readers who want to use R for statistical computation and simulation. We have also added a listing of discrete and continuous distributions in Appendix D. This will serve as a quick and helpful reference to the reader.
　　Content and Course Planning
　　Chapters i and 2 give the reader the necessary background material on probability and distribution theory for the remainder of the book. Chapter 3 discusses the most widely used discrete and continuous probability distributions. Chapter 4 contains topics in basic inference as described above. Chapter 5 presents large sample theory on convergence in probability and distribution and ends with the Central Limit Theorem. Chapter 6 provides a complete inference (estimation and testing) based on maximum likelihood theory. This chapter also contains a discussion of the EM algorithm and its application to several maximum likelihood situations. Chapters 7-8 contain material on sufficient statistics and optimal tests of hypotheses. The final three chapters provide theory for three important topics in statistics. Chapter 9 contains inference for normal theory methods for basic analysis of variance, univariate regression, and correlation models. Chapter 10 presents nonparametric methods (estimation and testing) for location and univariate regression models. It also includes discussion on the robust concepts of efficiency, influence, and breakdown.Chapter 11 offers an introduction to Bayesian methods. This includes traditional Bayesian procedures as well as Maxkov Chain Monte Carlo techniques.
　　Our text can be used in several different courses in mathematical statistics. A one-semester course would include most of the sections in Chapters 1-4. The second semester would usually consist of Chapters 5-8, although some instructors might prefer to use topics from Chapters 9-11. For example, a Bayesian advocate might want to teach Chapter 11 after Chapter 5, a nonparametrician could insert Chapter 10 earlier, or a traditional statistician would include topics from Chapter 9.Acknowledgements
　　We have many readers to thank. Their suggestions and comments proved invaluable in the preparation of this edition. A special thanks goes to Jun Yah of the University of Iowa, who made his web page on the sixth edition available to all, and also to Thomas Hettmansperger of Penn State University, Ash Abebe of Auburn University,and Bradford Crain of Portland State University for their helpful comments. We thank our accuracy checkers Kimberly F. Sellers (Georgetown University), Brian Newquist, Bill Josephson, and Joan Saniuk for their careful review. We would also like to thank the following reviewers for their comments and suggestions: Ralph Russo (University of Iowa), Kanapathi Thiru (University of Alaska), Lifang Hsu (Le Moyne College), and Xiao Wang (University of Maryland-Baltimore). Last, but not least, we must thank our wives, Ann and Marge, who provided great support for our efforts.
　　Bob Hogg & Joe McKean
　　

　　“该书写作风格极其清晰，就更高等内容的应用而言，我没有任何质疑。书中内容表述专业而现代，假如我有机会再次讲授数理统计学，我会毫不犹豫使用它，同时推荐给我的同事们。”
　　——Walter Freiberger，布朗大学
　　

　　插图：
　　1.4.27.Each bag in a large box contains 25 tulip bulbs.It is known that 60% of the bags contain bulbs for 5 red and 20 yellow tulips,while the remaining 40% of the bags contain bulbs for 15 red and 10 yellow tulips.A bag is selected at random and a bulb taken at random from this bag is planted.
　　(a)What is the probability that it will be a yellow tulip?
　　(b)Given that it is yellow,what is the conditional probability it comes from a bag that contained 5 red and 20 yellow bulbs?
　　1.4.28.A bowl contains 10 chips numbered 1,2,…,10,respectively.Five chips are drawn at random,one at a time,and without replacement.What is the probability that two even-numbered chips are drawn and they occur on even-numbered draws?
　　1.4.29.A person bets 1 dollar to b dollars that he can draw two cards from an ordinary deck of cards without replacement and that they will be of the same suit.Find b so that the bet is fair.1.4.30(Monte Hall Problem).Suppose there are three curtains.Behind one curtain there is a nice prize,while behind the other two there are worthless prizes.A contestant selects one curtain at random,and then Monte Hall opens one of the other two curtains to reveal a worthless prize.Hall then expresses the willingness to trade the curtain that the contestant has chosen for the other curtain that has not been opened.Should the contestant switch curtains or stick with the one that she has?To answer the question,determine the probability that she wins the prize if she switches.
　　1.4.31.A French nobleman,Chevalier de Méeré,had asked a famous mathematician,Pascal,to explain why the following two probabilities were different(the difference had been noted from playing the game many times):(1)at least one six in four independent casts of a six-sided die;(2)at least a pair of sixes in 24 independent casts of a pair of dice.From proportions it seemed to de Méré that the probabilities should be the same.Compute the probabilities of(1)and(2).
　　1.4.32.Hunters A and B shoot at a target;the probabilities of hitting the target are P1 and P2,respectively.Assuming independence,can P1 and P2 be selected so that
　　P(zero hits)= P(one hit)= P(two hits)?
　　1.4.33.At the beginning of a study of individuals,15% were classified as heavy smokers,30% were classified as light smokers,and 55% were classified as nonsmokers.In the five-year study,it was determined that the death rates of the heavy and light smokers were five and three times that of the nonsmokers,respectively.A randomly selected participant died over the five-year period: calculate the probability that the participant was a nonsmoker.
　　1.4.34.A chemist wishes to detect an impurity in a certain compound that she is making.There is a test that detects an impurity with probability 0.90;however,this test indicates that an impurity is there when it is not about 5% of the time.The chemist produces compounds with the impurity about 20% of the time.A compound is selected at random from the chemist's output.The test indicates that an impurity is present.What is the conditional probability that the compound actually has the impurity?
　　1.5 Random Variables
　　The reader perceives that a sample space C may be tedious to describe if the elements of C are not numbers.We now discuss how we may formulate a rule,or a set of rules,by which the elements c of C may be represented by numbers.We begin the discussion with a very simple example.Let the random experiment be the toss of a coin and let the sample space associated with the experiment be C={H,T},where H and T represent heads and tails,respectively.Let X be a function such that X(T)=0 and X(H)=1.Thus X is a real-valued function defined on the sample space C which takes us from the sample space C to a space of real numbers D={0,1}.We now formulate the definition of a random variable and its space.