數(shù)理統(tǒng)計學(xué)導(dǎo)論

內(nèi)容概要

　　這本經(jīng)典教材保持著一貫的風(fēng)格，清晰地闡述基本理論，并且為了更好地讓讀者理解數(shù)理統(tǒng)計，還提供了一些重要的背景材料。內(nèi)容覆蓋估計和測試方面的古典統(tǒng)計推斷方法，并深入介紹了充分性和測試理論，包括一致最佳檢驗和似然率。書中含有大量實例和練習(xí)，便于讀者理解和鞏固所學(xué)知識。

作者簡介

作者：（美國）霍格（Robert V.Hogg） （美國）Joseoh W.McKean （美國）Allen T.Craig  霍格（Robert V.Hogg），艾奧瓦大學(xué)統(tǒng)計與精算科學(xué)系教授，自1948年開始任教于艾奧瓦大學(xué)，在此從事教學(xué)和管理工作50多年，并幫助籌建了統(tǒng)計與精算科學(xué)系。他曾擔(dān)任美國統(tǒng)計協(xié)會（ASA）主席，獲得過包括美國數(shù)學(xué)協(xié)會杰出教育獎在內(nèi)的多項教學(xué)獎。 Joseph W.McKean，西密歇根大學(xué)統(tǒng)計系教授，ASA會士。他在線性、非線性、混合模型的穩(wěn)健非參數(shù)處理方面已發(fā)表多篇論文，主要講授統(tǒng)計學(xué)、概率論、統(tǒng)計方法、非參數(shù)理論等課程。 Allen T.Craig，艾奧瓦大學(xué)教授，已于1970年退休。他曾擔(dān)任美國數(shù)理統(tǒng)計學(xué)會（IMS）第一任秘書長，發(fā)起并參與了本書的撰寫工作。

書籍目錄

Preface 
1 Probability and Distributio
  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 naformatio
  1．7 Continuous Random Variables
    1．7．1 naDSformatio
  1．8 Expectation of a Random Variable
  1．9 Some Special Expectatio
  1．10 Important Inequalities
2 Multivariate Distributio
  2．1 Distributio of Two Random Variables
    2．1．1Expectation
  2．2 naformatio：Bivariate Random Variables
  2．3 Conditional Distributio and Expectatio
  2．4 The Correlation Coefficient
  2．5 Independent Random Variables
  2．6 Exteion to Several Random Variables
    2．6．1*Multivariate Variance-Covariance Matrix
  2．7 naformatio for Several Random Variables
  2．8 Linear Combinatio of Random Variables
3 Some Special Distributio
  3．1 The Binomial and Related Distributio
  3．2 The Poisson Distribution
  3．3 The Г，χ2，andβ Distributio
  3．4 The Normal Distribution
  3．4．1Contaminated Normals
  3．5 The Multivariate Normal Distribution
  3．5．1*Applicatio
  3．6 t-and F-Distributio
    3．6．1 The t-distribution
    3．6．2 The F-distribution
    3．6．3 Student’S Theorem
  3．7 Mixture Distributio
 4 Some Elementary Statistical Inferences
  4．1 Sampling and Statistics
    4．1．1 Histogram Estimates of pmfs and pdfs
  4．2 Confidence Intervals
    4．2．1Confidence Intervals for Difference in Mea
    4．2．2Confidence Interval for Difference in Proportio
  4．3 Confidence Intervals for Paramete of Discrete Distributio
  4．4 CIrder Statistics
  4．4．1Quantiles
  4．4．2Confidence Intervals for Quantiles
  4．5 Introduction to Hypothesis Testing
  4．6 Additional Comments About Statistical Tests
  4．7 Chi-Square Tests
  4．8 The Method of Monte Carlo
  4．8．1 Accept-Reject Generation Algorithm
  4．9 Bootstrap Procedures
  4．9．1 Percentile Bootstrap Confidence Intervals
  4．9．2Bootstrap Testing Procedures
  4．10 *Tolerance Limits for Distributio
5 Coistency and Limiting Distributio
  5．1 Convergence in Probability
  5．2 Convergence in Distribution
    5．2．1Bounded in Probability
    5．2．2 △-Method
    5．2．3 Moment Generating Function Technique
  5．3 Central Limit Theorem
  5．4 *Exteio to Multivariate Distributio
6 Maximum Likelihood Methods
  6．1 Maximum Likeli．hood Estimation
  6．2 Rao-Cram6r Lower Bound and E伍ciency
  6．3 Maximum Likelihood Tests
  6．4 Multiparameter Case：Estimation
  6．5 Multiparameter Case：Testing
  6．6 The EM Algorithm
7 Sufficiency
  7．1 Measures of Quality of Estimato
  7．2 A Su伍cient Statistic for a Parameter
  7．3 Properties of a Sufficient Statistic
  7．4 Completeness and Uniqueness
  7．5 The Exponential Class of Distributio
  7．6 Functio of a Parameter
  7．7 The Cuse of Several Paramete
  7．8 Minimal Sufficiency and Ancillary Statistics
  7．9 Sufficiency,Completeness．a(chǎn)nd Independence
8 Optimal Tests of Hypotheses
  8．1 Most Powerful Tests
  8．2 Uniformly Most Powerful Tests
  8．3 Likelihood Ratio Tests
  8．4 The Sequential Probability Ratio Test
  8．5Minimax and Classification Procedures
    8．5．1 Minimax Procedures
    8．5．2 Classification
9 Inferences About Normal MOdels
  9．1 Quadratic Forms
  9．2 One-Way ANOVA
  9．3 Noncentralχ2and F-Distributio
  9．4 Multiple Compariso
  9．5 The Analysis of Variance
  9．6 A Regression Problem
  9．7 A Test of Independence
  9．8 The Distributio of Certain Quadratic Forms
  9．9 The Independence of Certain Quadratic Forills
10 Nonparametric and Robust Statistics
  10．1 Location Models
  10．2 Sample Median and the Sign Test
  10．2．1 Asymptotic Relative Efficiency
  10．2．2 Estimating Equatio Based on the Sign Test
  10．2．3 Confidence Interval for the Median
  10．3 Signed-Rank Wilcoxon
    10．3．1 Asymptotic Relative Emciency
    10．3．2 Estimating Equatio Based on Signed-Rank Wilcoxon
    10．3．3 Confidence Interval for the Median
  10．4 Mann-Whitnev-Wilcoxon Procedure
    10．4．1 Asymptotic Relative Efficiency
    10．4．2 Estimating Equatio Based on the Mann-Whitney-Wilcoxon
    10．4．3 Confidence Interval for the Shift Parameter △
  10．5 General Rank Scores
    10．5．1 Efficacy
    10．5．2 Estimating Equatio Based on General Scores
    10．5．3 0ptimization：Best Estimates
  10．6 Adaptive Procedures
  10．7 Simple Linear Model
  10．8 Measures of Association
    10．8．1 Kendall’S т
    10．8．2 Spearman’S Rho
  10．9 Robust Concepts
    10．9．1 Location Model
    10．9．2 Linear Model
11 Bayesian Statistics
  11．1 Subjective Probability
  11．2 Bayesian Procedures
    11．2．1 Prior and Posterior Distributio
    11．2．2 Bayesian Point Estimation
    11．2．3 Bayesian Interval Estimation
    11．2．4 Bayesian Testing Procedures
    11．2．5 Bayesian Sequential Procedures
  11．3 More Bayesian Terminology and Ideas
  11．4 Gibbs Sampler
  11．5 Modern Bayesian Methods
    11．5．1 Empirical Bayes
A Mathematical Comments
  A．1 Regularity Conditio
  A．2 Sequences
B R Functio
C Tables of Distributio
D Lists of Common Distributio
E References
F Awe to Selected Exercisds
  Index

章節(jié)摘錄

版權(quán)頁：   插圖：   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.

編輯推薦

《數(shù)理統(tǒng)計學(xué)導(dǎo)論(英文版?第7版)》是數(shù)理統(tǒng)計方面的一本經(jīng)典教材，自1959年出版以來，廣受讀者好評，并被眾多院校選為教材，如布朗大學(xué)、喬治華盛頓大學(xué)等。第7版延續(xù)了前幾版的一貫風(fēng)格，清晰而全面地闡述了數(shù)理統(tǒng)計的基本理論，并且為了讓讀者更好地理解數(shù)理統(tǒng)計，還提供了豐富的例子和一些重要的背景材料。

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“該書寫作風(fēng)格極其清晰，就更高等內(nèi)容的應(yīng)用而言，我沒有任何質(zhì)疑。書中內(nèi)容表述專業(yè)而現(xiàn)代，假如我有機會再次講授數(shù)理統(tǒng)計學(xué)，我會毫不猶豫使用它，同時推薦給我的同事們。” ——Walter Freiberger，布朗大學(xué)

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