Statistical inference / Vijay K. Rohatgi.
Series Wiley series in probability and mathematical statisticsProbability and mathematical statisticsEditor: New York : Wiley, c1984Descripción: xiv, 940 p. : il. ; 24 cmISBN: 0471871265Tema(s): Mathematical statisticsOtra clasificación: 62-01 Recursos en línea: Google Book SearchCHAPTER 1. INTRODUCTION [1] 1.1 Introduction [1] 1.2 Stochastic Models [1] 1.3 Probability, Statistics, and Inference [5] CHAPTER 2. PROBABILITY MODEL [8] 2.1 Introduction [8] 2.2 Sample Space and Events [8] 2.3 Probability Axioms [16] 2.4 Elementary Consequences of Axioms [26] 2.5 Counting Methods [33] 2.6 Conditional Probability [44] 2.7 Independence [56] 2.8 Simple Random Sampling from a Finite Population [67] 2.9 Review Problems [75] CHAPTER 3. PROBABILITY DISTRIBUTIONS [80] 3.1 Introduction [80] 3.2 Random Variables and Random Vectors [81] 33 Describing a Random Variable [88] 3.4 Multivariate Distributions [105] 3.5 Marginal and Conditional Distributions [120] 3.6 Independent Random Variables [139] 3.7 Numerical Characteristics of a Distribution—Expected Value [150] 3.8 Random Sampling from a Probability Distribution [171] 3.9 Review Problems [182] CHAPTER 4. INTRODUCTION TO STATISTICAL INFERENCE [185] 4.1 Introduction [185] 4.2 Parametric and Nonparametric Families [186] 4.3 Point and Interval Estimation [188] 4.4 Testing Hypotheses [209] 4.5 Fitting the Underlying Distribution [230] 4.6 Review Problems [241] CHAPTER 5. MORE ON MATHEMATICAL EXPECTATION [244] 5.1 Introduction [244] 5.2 Moments in the Multivariate Case [244] 53 Linear Combinations of Random Variables [257] 5.4 The Law of Large Numbers [274] 5.5* Conditional Expectation [279] 5.6 Review Problems [293] CHAPTER 6. SOME DISCRETE MODELS [297] 6.1 Introduction’ [297] 6.2 Discrete Uniform Distribution [298] 63 Bernoulli and Binomial Distributions [304] 6.4 Hypergeometric Distribution [335] 6.5 Geometric and Negative Binomial Distributions: Discrete Waiting-Time Distribution [354] 6.6 Poisson Distribution [369] 6.7 Multivariate Hypergeometric and Multinomial Distributions [379] 6.8 Review Problems [387] CHAPTER 7. SOME CONTINUOUS MODELS [390] 7.1 Introduction [390] 7.2 Uniform Distribution [390] 73* Gamma and Beta Functions [398] 7.4 Exponential, Gamma, and Weibull Distributions [403] 7.5* Beta Distribution [416] 7.6 Normal Distribution [421] 7.7* Bivariate Normal Distribution [433] 7.8 Review Problems [440] CHAPTER 8. FUNCTIONS OF RANDOM VARIABLES AND RANDOM VECTORS [443] 8.1 Introduction [443] 8.2 The Method of Distribution Functions [445] 8.3* The Method of Transformations [464] 8.4 Distributions of Sum, Product, and Quotient of Two Random Variables [473] 8.5 Order Statistics [488] 8.6* Generating Functions [505] 8.7 Sampling From a Normal Population [522] 8.8 Review Problems [549] CHAPTER 9. LARGE-SAMPLE THEORY [555] 9.1 Introduction [555] 9.2 Approximating Distributions: Limiting Moment Generating Function [556] 9.3 The Central Limit Theorem of Lévy [560] 9.4 The Normal Approximation to Binomial, Poisson, and Other Integer-Valued Random Variables [579] 9.5 Consistency [591] 9.6 Large-Sample Point and Interval Estimation [595] 9.7 Large-Sample Hypothesis Testing [606] 9.8 Inference Concerning Quantiles [616] 9.9 Goodness of Fit for Multinomial Distribution: Prespecified Cell Probabilities [624] 9.10 Review Problems [635] CHAPTER 10. GENERAL METHODS OF POINT AND INTERVAL ESTIMATION [640] 10.1 Introduction [640] 10.2 Sufficiency [641] 10.3 Unbiased Estimation [652] 10.4 The Substitution Principle (The Method of Moments) [664] 10.5 Maximum Likelihood Estimation [671] 10.6* Bayesian Estimation [684] 10.7 Confidence Intervals [694] 10.8 Review Problems [704] CHAPTER 11. TESTING HYPOTHESES [708] 11.1 Introduction [708] 11.2 Neyman-Pearson Lemma [709] 113* Composite Hypotheses [716] 11.4* Likelihood Ratio Tests [720] 11.5 The Wilcoxon Signed Rank Test [727] 11.6 Some Two-Sample Tests [735] 11.7 Chi-Square Test of Goodness of Fit Revisited [747] 11.8* Kolmogorov-Smirnov Goodness of Fit Test [754] 11.9 Measures of Association for Bivariate Data [762] 11.10 Review Problems [774] CHAPTER 12. ANALYSIS OF CATEGORICAL DATA [780] 12.1 Introduction [739] 12.2 Chi-Square Test for Homogeneity [780] 12.3 Testing Independence in Contingency Tables [791] 12.4 Review Problems [798] CHAPTER 13. ANALYSIS OF VARIANCE: ^-SAMPLE PROBLEMS [801] 13.1 Introduction [801] 13.2 One-Way Analysis of Variance [802] 13.3 Multiple Comparison of Means [816] 13.4 Two-Way Analysis of Variance [822] 13.5 Testing Equality in K-Independent Samples: Nonnormal Case [842] 13.6 The Friedman Test for k-Related Samples [854] 13.7 Review Problems [864] APPENDIX-TABLES [870] ANSWERS TO ODD-NUMBERED PROBLEMS [914] INDEX [933]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 62 R737 (Browse shelf) | Available | A-5915 |
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CHAPTER 1. INTRODUCTION --
[1] --
1.1 Introduction [1] --
1.2 Stochastic Models [1] --
1.3 Probability, Statistics, and Inference [5] --
CHAPTER 2. PROBABILITY MODEL [8] --
2.1 Introduction [8] --
2.2 Sample Space and Events [8] --
2.3 Probability Axioms [16] --
2.4 Elementary Consequences of Axioms [26] --
2.5 Counting Methods [33] --
2.6 Conditional Probability [44] --
2.7 Independence [56] --
2.8 Simple Random Sampling from a Finite Population [67] --
2.9 Review Problems [75] --
CHAPTER 3. PROBABILITY DISTRIBUTIONS [80] --
3.1 Introduction [80] --
3.2 Random Variables and Random Vectors [81] --
33 Describing a Random Variable [88] --
3.4 Multivariate Distributions [105] --
3.5 Marginal and Conditional Distributions [120] --
3.6 Independent Random Variables [139] --
3.7 Numerical Characteristics of a Distribution—Expected Value [150] --
3.8 Random Sampling from a Probability Distribution [171] --
3.9 Review Problems [182] --
CHAPTER 4. INTRODUCTION TO STATISTICAL INFERENCE [185] --
4.1 Introduction [185] --
4.2 Parametric and Nonparametric Families [186] --
4.3 Point and Interval Estimation [188] --
4.4 Testing Hypotheses [209] --
4.5 Fitting the Underlying Distribution [230] --
4.6 Review Problems [241] --
CHAPTER 5. MORE ON MATHEMATICAL EXPECTATION [244] --
5.1 Introduction [244] --
5.2 Moments in the Multivariate Case [244] --
53 Linear Combinations of Random Variables [257] --
5.4 The Law of Large Numbers [274] --
5.5* Conditional Expectation [279] --
5.6 Review Problems [293] --
CHAPTER 6. SOME DISCRETE MODELS [297] --
6.1 Introduction’ [297] --
6.2 Discrete Uniform Distribution [298] --
63 Bernoulli and Binomial Distributions [304] --
6.4 Hypergeometric Distribution [335] --
6.5 Geometric and Negative Binomial Distributions: Discrete Waiting-Time Distribution [354] --
6.6 Poisson Distribution [369] --
6.7 Multivariate Hypergeometric and Multinomial Distributions [379] --
6.8 Review Problems [387] --
CHAPTER 7. SOME CONTINUOUS MODELS [390] --
7.1 Introduction [390] --
7.2 Uniform Distribution [390] --
73* Gamma and Beta Functions [398] --
7.4 Exponential, Gamma, and Weibull Distributions [403] --
7.5* Beta Distribution [416] --
7.6 Normal Distribution [421] --
7.7* Bivariate Normal Distribution [433] --
7.8 Review Problems [440] --
CHAPTER 8. FUNCTIONS OF RANDOM VARIABLES AND RANDOM VECTORS [443] --
8.1 Introduction [443] --
8.2 The Method of Distribution Functions [445] --
8.3* The Method of Transformations [464] --
8.4 Distributions of Sum, Product, and Quotient of Two Random Variables [473] --
8.5 Order Statistics [488] --
8.6* Generating Functions [505] --
8.7 Sampling From a Normal Population [522] --
8.8 Review Problems [549] --
CHAPTER 9. LARGE-SAMPLE THEORY [555] --
9.1 Introduction [555] --
9.2 Approximating Distributions: Limiting Moment Generating Function [556] --
9.3 The Central Limit Theorem of Lévy [560] --
9.4 The Normal Approximation to Binomial, Poisson, and Other Integer-Valued Random Variables [579] --
9.5 Consistency [591] --
9.6 Large-Sample Point and Interval Estimation [595] --
9.7 Large-Sample Hypothesis Testing [606] --
9.8 Inference Concerning Quantiles [616] --
9.9 Goodness of Fit for Multinomial Distribution: Prespecified Cell Probabilities [624] --
9.10 Review Problems [635] --
CHAPTER 10. GENERAL METHODS OF POINT AND INTERVAL ESTIMATION [640] --
10.1 Introduction [640] --
10.2 Sufficiency [641] --
10.3 Unbiased Estimation [652] --
10.4 The Substitution Principle (The Method of Moments) [664] --
10.5 Maximum Likelihood Estimation [671] --
10.6* Bayesian Estimation [684] --
10.7 Confidence Intervals [694] --
10.8 Review Problems [704] --
CHAPTER 11. TESTING HYPOTHESES [708] --
11.1 Introduction [708] --
11.2 Neyman-Pearson Lemma [709] --
113* Composite Hypotheses [716] --
11.4* Likelihood Ratio Tests [720] --
11.5 The Wilcoxon Signed Rank Test [727] --
11.6 Some Two-Sample Tests [735] --
11.7 Chi-Square Test of Goodness of Fit Revisited [747] --
11.8* Kolmogorov-Smirnov Goodness of Fit Test [754] --
11.9 Measures of Association for Bivariate Data [762] --
11.10 Review Problems [774] --
CHAPTER 12. ANALYSIS OF CATEGORICAL DATA [780] --
12.1 Introduction [739] --
12.2 Chi-Square Test for Homogeneity [780] --
12.3 Testing Independence in Contingency Tables [791] --
12.4 Review Problems [798] --
CHAPTER 13. ANALYSIS OF VARIANCE: ^-SAMPLE PROBLEMS [801] --
13.1 Introduction [801] --
13.2 One-Way Analysis of Variance [802] --
13.3 Multiple Comparison of Means [816] --
13.4 Two-Way Analysis of Variance [822] --
13.5 Testing Equality in K-Independent Samples: Nonnormal Case [842] --
13.6 The Friedman Test for k-Related Samples [854] --
13.7 Review Problems [864] --
APPENDIX-TABLES [870] --
ANSWERS TO ODD-NUMBERED PROBLEMS [914] --
INDEX [933] --
MR, 86a:62003
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