Normal view

## 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 Search
Contenidos:
```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]
INDEX [933]```
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Libros
Libros ordenados por tema 62 R737 (Browse shelf) Available A-5915

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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