An introduction to probability theory and mathematical statistics / V. K. Rohatgi.
Series Wiley series in probability and mathematical statisticsEditor: New York : Wiley, c1976Descripción: xiv, 684 p. ; 24 cmISBN: 0471731358Tema(s): Probabilities | Mathematical statisticsOtra clasificación: 60-01 (62-01)P. 1 Sets and Classes [1] P.2 Calculus [3] P. 3 Linear Algebra [15] 1 Probability 1.1 Introduction [18] 1.2 Sample Space [19] 1.3 Probability Axioms [24] 1.4 Combinatorics: Probability on Finite Sample Spaces [35] 1.5 Conditional Probability and Bayes Theorem [40] 1.6 Independence of Events [45] 2 Random Variables and Their Probability Distributions 2.1 Introduction [52] 2.2 Random Variables [52] 2.3 Probability Distribution of a Random Variable [56] 2.4 Discrete and Continuous Random Variables [61] 2.5 Functions of a Random Variable [67] 3 Moments and Generating Functions 3.1 Introduction [78] 3.2 Moments of a Distribution Function [78] 3.3 Generating Functions [93] 3.4 Some Moment Inequalities [100] 4 Random Vectors 4.1 Introduction [105] 4.2 Random Vectors [105] 4.3 Independent Random Variables [119] 4.4 Functions of Random Vectors [127] 4.5 Order Statistics and Their Distributions [149] 4.6 Moments and Moment Generating Functions [154] 4.7 Conditional Expectation [167] 4.8 The Principle of Least Squares [172] 5 Some Special Distributions 5.1 Introduction [181] 5.2 Some Discrete Distributions [181] 5.3 Some Continuous Distributions [203] 5.4 The Bivariate and Multivariate Normal Distributions [227] 5.5 The Exponential Family of Distributions [236] 6 Limit Theorems 6.1 Introduction [240] 6.2 Modes of Convergence [240] 6.3 The Weak Law of Large Numbers [257] 6.4 The Strong Law of Large Numbers [263] 6.5 Limiting Moment Generating Functions [276] 6.6 The Central Limit Theorem [280] 7 Sample Moments and Their Distributions 7.1 Introduction [296] 7.2 Random Sampling [297] 7.3 Sample Characteristics and Their Distributions [299] 7.4 Chi-Square, F, and F-Distributions: Exact Sampling Distributions [311] 7.5 The Distribution of (X, S2) in Sampling from a Normal Population [321] 7.6 Sampling from a Bivariate Normal Distribution [325] 8 The Theory of Point Estimation 8.1 Introduction [333] 8.2 The Problem of Point Estimation [333] 8.3 Properties of Estimates [335] 8.4 Unbiased Estimation [350] 8.5 Unbiased Estimation (Continued): A Lower Bound for the Variance of an Estimate [361] 8.6 The Method of Moments [373] 8.7 Maximum Likelihood Estimates [375] 8.8 Bayes and Minimax Estimation [388] 8.9 Minimal Sufficient Statistic [399] 9 Neyman-Pearson Theory of Testing of Hypotheses 9.1 Introduction [404] 9.2 Some Fundamental Notions of Hypotheses Testing [404] 9.3 The Neyman-Pearson Lemma [412] 9.4 Families with Monotone Likelihood Ratio [418] 9.5 Unbiased and Invariant Tests [425] 10 Some Further Results on Hypotheses Testing 10.1 Introduction [435] 10.2 The Likelihood Ratio Tests [435] 10.3 The Chi-Square Tests [444] 10.4 The t-tests [452] 10.5 The F-tests [457] 10.6 Bayes and Minimax Procedures [459] 11 Confidence Estimation 11.1 Introduction [466] 11.2 Some Fundamental Notions of Confidence Estimation [466] 11.3 Shortest-Length Confidence Intervals [479] 11.4 Relation Between Confidence Estimation and Hypotheses Testing [485] 11.5 Unbiased Confidence Intervals [490] 11.6 Bayes Confidence Intervals [494] 12 The General Linear Hypothesis 12.1 Introduction [497] 12.2 The General Linear Hypothesis [497] 12.3 The Regression Model [506] 12.4 One-Way Analysis of Variance [513] 12.5 Two-Way Analysis of Variance with One Observation per Cell [518] 12.6 Two-Way Analysis of Variance with Interaction [524] 13 Nonparametric Statistical Inference 13.1 Introduction [530] 13.2 Nonparametric Estimation [531] 13.3 Some Single-Sample Problems [538] 13.4 Some Two-Sample Problems [553] 13.5 Tests of Independence [564] 13.6 Some Uses of Order Statistics [575] 13.7 Robustness [580] 14 Sequential Statistical Inference 14.1 Introduction [589] 14.2 Some Fundamental Ideas of Sequential Sampling [589] 14.3 Sequential Unbiased Estimation [596] 14.4 Sequential Estimation of the Mean of a Normal Population [602] 14.5 The Sequential Probability Ratio Test [612] 14.6 Some Properties of the Sequential Probability Ratio Test [620] 14.7 The Fundamental Identity of Sequential Analysis and Its Applications [633]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 60 R737 (Browse shelf) | Available | A-7483 |
Incluye referencias bibliográficas (p. 641-647) e índices.
P. 1 Sets and Classes [1] --
P.2 Calculus [3] --
P. 3 Linear Algebra [15] --
1 Probability --
1.1 Introduction [18] --
1.2 Sample Space [19] --
1.3 Probability Axioms [24] --
1.4 Combinatorics: Probability on Finite Sample Spaces [35] --
1.5 Conditional Probability and Bayes Theorem [40] --
1.6 Independence of Events [45] --
2 Random Variables and Their Probability Distributions --
2.1 Introduction [52] --
2.2 Random Variables [52] --
2.3 Probability Distribution of a Random Variable [56] --
2.4 Discrete and Continuous Random Variables [61] --
2.5 Functions of a Random Variable [67] --
3 Moments and Generating Functions --
3.1 Introduction [78] --
3.2 Moments of a Distribution Function [78] --
3.3 Generating Functions [93] --
3.4 Some Moment Inequalities [100] --
4 Random Vectors --
4.1 Introduction [105] --
4.2 Random Vectors [105] --
4.3 Independent Random Variables [119] --
4.4 Functions of Random Vectors [127] --
4.5 Order Statistics and Their Distributions [149] --
4.6 Moments and Moment Generating Functions [154] --
4.7 Conditional Expectation [167] --
4.8 The Principle of Least Squares [172] --
5 Some Special Distributions --
5.1 Introduction [181] --
5.2 Some Discrete Distributions [181] --
5.3 Some Continuous Distributions [203] --
5.4 The Bivariate and Multivariate Normal Distributions [227] --
5.5 The Exponential Family of Distributions [236] --
6 Limit Theorems --
6.1 Introduction [240] --
6.2 Modes of Convergence [240] --
6.3 The Weak Law of Large Numbers [257] --
6.4 The Strong Law of Large Numbers [263] --
6.5 Limiting Moment Generating Functions [276] --
6.6 The Central Limit Theorem [280] --
7 Sample Moments and Their Distributions --
7.1 Introduction [296] --
7.2 Random Sampling [297] --
7.3 Sample Characteristics and Their Distributions [299] --
7.4 Chi-Square, F, and F-Distributions: Exact Sampling --
Distributions [311] --
7.5 The Distribution of (X, S2) in Sampling from a Normal --
Population [321] --
7.6 Sampling from a Bivariate Normal Distribution [325] --
8 The Theory of Point Estimation --
8.1 Introduction [333] --
8.2 The Problem of Point Estimation [333] --
8.3 Properties of Estimates [335] --
8.4 Unbiased Estimation [350] --
8.5 Unbiased Estimation (Continued): A Lower Bound for the Variance of an Estimate [361] --
8.6 The Method of Moments [373] --
8.7 Maximum Likelihood Estimates [375] --
8.8 Bayes and Minimax Estimation [388] --
8.9 Minimal Sufficient Statistic [399] --
9 Neyman-Pearson Theory of Testing of Hypotheses --
9.1 Introduction [404] --
9.2 Some Fundamental Notions of Hypotheses Testing [404] --
9.3 The Neyman-Pearson Lemma [412] --
9.4 Families with Monotone Likelihood Ratio [418] --
9.5 Unbiased and Invariant Tests [425] --
10 Some Further Results on Hypotheses Testing --
10.1 Introduction [435] --
10.2 The Likelihood Ratio Tests [435] --
10.3 The Chi-Square Tests [444] --
10.4 The t-tests [452] --
10.5 The F-tests [457] --
10.6 Bayes and Minimax Procedures [459] --
11 Confidence Estimation --
11.1 Introduction [466] --
11.2 Some Fundamental Notions of Confidence Estimation [466] --
11.3 Shortest-Length Confidence Intervals [479] --
11.4 Relation Between Confidence Estimation and Hypotheses Testing [485] --
11.5 Unbiased Confidence Intervals [490] --
11.6 Bayes Confidence Intervals [494] --
12 The General Linear Hypothesis --
12.1 Introduction [497] --
12.2 The General Linear Hypothesis [497] --
12.3 The Regression Model [506] --
12.4 One-Way Analysis of Variance [513] --
12.5 Two-Way Analysis of Variance with One Observation per Cell [518] --
12.6 Two-Way Analysis of Variance with Interaction [524] --
13 Nonparametric Statistical Inference --
13.1 Introduction [530] --
13.2 Nonparametric Estimation [531] --
13.3 Some Single-Sample Problems [538] --
13.4 Some Two-Sample Problems [553] --
13.5 Tests of Independence [564] --
13.6 Some Uses of Order Statistics [575] --
13.7 Robustness [580] --
14 Sequential Statistical Inference --
14.1 Introduction [589] --
14.2 Some Fundamental Ideas of Sequential Sampling [589] --
14.3 Sequential Unbiased Estimation [596] --
14.4 Sequential Estimation of the Mean of a Normal Population [602] --
14.5 The Sequential Probability Ratio Test [612] --
14.6 Some Properties of the Sequential Probability Ratio Test [620] --
14.7 The Fundamental Identity of Sequential Analysis and Its Applications [633] --
MR, 53 #11684
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