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图书信息
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数理统计:英文版
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ISBN: | 9787030670007 |
定价: | ¥99.00 |
作者: | 田国梁,蒋学军编著 |
出版社: | 科学出版社 |
出版时间: | 2021年01月 |
开本: | 24cm |
页数: | 320页 |
装祯: | 平装 |
中图法: | O212 |
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其它供货商库存合计
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390
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2024-03-29
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图书简介 | 本书主要内容包括:概率和分布、抽样分布、点估计、区间估计、假设检验、斜零分布的临界区域和p值等。 |
目录 | Preface Chapter1 Probabilityand Distributionr/> 1.1 Probability 1.1.1 Permutation, combination and binomial coefficientr/> 1.1.2 Sample space 1.1.3 Eventr/> 1.1.4 Propertiesof probability 1.2 Conditional Probability 1.3 Bayes Theorem 1.4 ProbabilityDistributionr/> 1.5 Bivariate Distributionr/> 1.5.1 Joint distribution 1.5.2 Marginal and conditional distributionr/> 1.5.3 Independencyoftwo randomvariabler/> 1.6 Expectation,Variance and Momentr/> 1.6.1 Momentr/> 1.6.2 Some probabilityinequalitier/> 1.6.3 Conditional expectation 1.6.4 Compound randomvariabler/> 1.6.5 Calculation of (conditional) probabilityvia (conditional) expectation 1.7 Moment GeneratingFunction 1.8 Beta and Gamma Distributionr/> 1.8.1 Beta distribution 1.8.2 Gamma distribution 1.9 Bivariate Normal Distribution 1.9.1 Univariate normal distribution 1.9.2 Correlation coefficient 1.9.3 Joint density 1.9.4 Stochastic representation of random variables or random vectorr/> Contents 1.10 Inverse Bayes Formulae 1.10.1 Three inverse Bayes formulae 1.10.2 Understanding the IBF 1.10.3 Two exampler/> 1.11 Categorical Distribution 1.12 Zero-inflatedPoisson Distribution Exercir/>Chapter2 Sampling Distributionr/> 2.1 Distribution of the Function of RandomVariabler/> 2.1.1 Cumulative distribution function technique 2.1.2 Transformation technique 2.1.3 Momentgenerating function technique 2.2 Statistics, Sample Mean and SampleVariance 2.2.1 Distributionofthe sample mean 2.2.2 Distributionofthe samplevariance 2.3 The and Distributionr/> 2.3.1 The distribution 2.3.2 The distribution 2.4 Order Statisticr/> 2.4.1 Distributionofa single order statistic 2.4.2 Joint distributionof more order statisticr/> 2.5 Limit Theoremr/> 2.5.1 Convergencyofa sequenceof distribution functionr/> 2.5.2 Convergencein probability 2.5.3 Relationshipof four classesof convergency 2.5.4 Lawof largenumber 2.5.5 Central limit theorem 2.6 Some Challenging Questionr/> Exercir/>Chapter3 Point Estimation 3.1 Maximum LikelihoodEstimator 3.1.1 Pointestimator andpointestimate 3.1.2 Joint densityand likelihoodfunction 3.1.3 Maximum likelihoodestimate and maximum likelihood estimator 3.1.4 Theinvariance propertyof MLE Contents vii 3.2 Moment Estimator 3.3 Bayesian Estimator 3.4 Propertiesof Estimatorr/> 3.4.1 Unbiasedner/> 3.4.2 Efficiency 3.4.3 Sufficiency 3.4.4 Completener/> 3.5 Limiting Properties of MLE 3.6 Some Challenging Questionr/> Exercir/>Chapter4 Confidence Interval Estimation 4.1 Introduction 4.2 The ConfidenceIntervalof Normal Mean 4.2.1 Thevarianceisknown 4.2.2 Thevarianceis unknown 4.3 The Confidence Interval of the Difference of Two Normal Meanr/> 4.4 The ConfidenceInterval of Normal Variance 4.4.1 The mean is known 4.4.2 The meanis unknown 4.5 The Confidence Interval of the Ratio of Two Normal Variancer/> 4.6 Large-Sample ConfidenceIntervalr/> 4.7 The Shortest ConfidenceInterval Exercir/>Chapter5 Hypothesis Testing 5.1 Introduction 5.1.1 Several basic notionr/> 5.1.2 TypeIerror andTypeII error 5.1.3 Power function 5.2 The Neyman–Pearson Lemma 5.2.1 Simplenullhypothesisversus simple alternative 5.2.2 Compositehypotheser/> 5.3 LikelihoodRatioTer/> 5.3.1 Likelihoodratio statistic 5.3.2 Likelihoodratio ter/> 5.4 Testson Normal Meanr/> 5.4.1 One–sample normal test whenvarianceisknown 5.4.2 One–sample ter/> 5.4.3 Two–samplet ter/> 5.5 GoodnessofFitTer/> 5.5.1 Introduction 5.5.2 Thechi-square testfor totallyknown distribution 5.5.3 The chi-square test for known distribution family with unknown parameterr/> Exercir/>Chapter6 Critical Regions and p-values for Skew Null Distributionr/> 6.1 One–sample Chi-square Test on Normal Variance 6.2 Two–sampleF Test on Normal Variancer/>Appendix A Basic Statistical Distributionr/> A.Discrete Distributionr/> A.Continuous Distributionr/>Appendix B AUnified Expectation Technique B.Continuous RandomVariabler/> B.Discrete RandomVariabler/>Appendix C The Newton–Raphson and Fisher Scoring Algorithmr/> C.Newton’s Method fo rRoot Finding C.Newton’s Method for CalculatingMLE C.The Newton–Raphson Algorithm for High-dimensional Caser/> C.The Fisher Scoring Algorithm List of Figurer/>List ofTabler/>List ofAcronymr/>List of Symbolr/>Referencer/>Subject Index
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