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Probability and statistical inference / / Robert Bartoszynski, Magdalena Niewiadomska-Bugaj
| Probability and statistical inference / / Robert Bartoszynski, Magdalena Niewiadomska-Bugaj |
| Autore | Bartoszynski Robert |
| Edizione | [3rd ed] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2021] |
| Descrizione fisica | 1 online resource (595 pages) |
| Disciplina | 519.54 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico | Probabilities |
| ISBN |
1-119-24381-5
1-119-24382-3 1-119-24383-1 |
| Classificazione |
417.1
519.54 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- Preface to Third Edition -- Preface to Second Edition -- About the Companion Website -- Chapter 1 Experiments, Sample Spaces, and Events -- 1.1 Introduction -- 1.2 Sample Space -- 1.3 Algebra of Events -- 1.4 Infinite Operations on Events -- Chapter 2 Probability -- 2.1 Introduction -- 2.2 Probability as a Frequency -- 2.3 Axioms of Probability -- 2.4 Consequences of the Axioms -- 2.5 Classical Probability -- 2.6 Necessity of the Axioms* -- 2.7 Subjective Probability* -- Chapter 3 Counting -- 3.1 Introduction -- 3.2 Product Sets, Orderings, and Permutations -- 3.3 Binomial Coefficients -- 3.4 Multinomial Coefficients -- Chapter 4 Conditional Probability, Independence, and Markov Chains -- 4.1 Introduction -- 4.2 Conditional Probability -- 4.3 Partitions -- Total Probability Formula -- 4.4 Bayes' Formula -- 4.5 Independence -- 4.6 Exchangeability -- Conditional Independence -- 4.7 Markov Chains* -- Chapter 5 Random Variables: Univariate Case -- 5.1 Introduction -- 5.2 Distributions of Random Variables -- 5.3 Discrete and Continuous Random Variables -- 5.4 Functions of Random Variables -- 5.5 Survival and Hazard Functions -- Chapter 6 Random Variables: Multivariate Case -- 6.1 Bivariate Distributions -- 6.2 Marginal Distributions -- Independence -- 6.3 Conditional Distributions -- 6.4 Bivariate Transformations -- 6.5 Multidimensional Distributions -- Chapter 7 Expectation -- 7.1 Introduction -- 7.2 Expected Value -- 7.3 Expectation as an Integral* -- Riemann Integral -- Lebesque Integral -- Riemann-Stieltjes Integral -- Lebesque-Stieltjes Integral -- Lebesque Integral: General Case -- 7.4 Properties of Expectation -- 7.5 Moments -- 7.6 Variance -- 7.7 Conditional Expectation -- 7.8 Inequalities -- Chapter 8 Selected Families of Distributions -- 8.1 Bernoulli Trials and Related Distributions.
Binomial Distribution -- Geometric Distribution -- Negative Binomial Distribution -- 8.2 Hypergeometric Distribution -- 8.3 Poisson Distribution and Poisson Process -- 8.4 Exponential, Gamma, and Related Distributions -- 8.5 Normal Distribution -- 8.6 Beta Distribution -- Chapter 9 Random Samples -- 9.1 Statistics and Sampling Distributions -- 9.2 Distributions Related to Normal -- 9.3 Order Statistics -- 9.4 Generating Random Samples -- 9.5 Convergence -- Weak Laws of Large Numbers -- Strong Laws of Large Numbers -- 9.6 Central Limit Theorem -- Chapter 10 Introduction to Statistical Inference -- 10.1 Overview -- 10.2 Basic Models -- 10.3 Sampling -- 10.4 Measurement Scales -- Chapter 11 Estimation -- 11.1 Introduction -- 11.2 Consistency -- 11.3 Loss, Risk, and Admissibility -- 11.4 Efficiency -- 11.5 Methods of Obtaining Estimators -- Method of Moments Estimators -- Maximum Likelihood Estimators -- Least Squares Estimators -- Robust Estimators -- 11.6 Sufficiency -- 11.7 Interval Estimation -- Confidence Intervals -- Bootstrap Intervals -- Chapter 12 Testing Statistical Hypotheses -- 12.1 Introduction -- 12.2 Intuitive Background -- 12.3 Most Powerful Tests -- 12.4 Uniformly Most Powerful Tests -- 12.5 Unbiased Tests -- 12.6 Generalized Likelihood Ratio Tests -- 12.7 Conditional Tests -- 12.8 Tests and Confidence Intervals -- 12.9 Review of Tests for Normal Distributions -- One‐Sample Procedures -- Hypotheses About the Variance, Mean Known -- Hypotheses About the Variance, Mean Unknown -- Two‐Sample Procedures -- Large Sample Tests for Binomial Distribution -- 12.10 Monte Carlo, Bootstrap, and Permutation Tests -- Monte Carlo Tests -- Bootstrap Tests -- Permutation Tests -- Chapter 13 Linear Models -- 13.1 Introduction -- 13.2 Regression of the First and Second Kind -- 13.3 Distributional Assumptions -- 13.4 Linear Regression in the Normal Case. 13.5 Testing Linearity -- 13.6 Prediction -- 13.7 Inverse Regression -- 13.8 BLUE -- 13.9 Regression Toward the Mean -- 13.10 Analysis of Variance -- 13.11 One‐Way Layout -- 13.12 Two‐Way Layout -- 13.13 ANOVA Models with Interaction -- 13.14 Further Extensions -- Chapter 14 Rank Methods -- 14.1 Introduction -- 14.2 Glivenko-Cantelli Theorem -- 14.3 Kolmogorov-Smirnov Tests -- One‐Sample Kolmogorov-Smirnov Test -- Two‐Sample Kolmogorov-Smirnov Test -- 14.4 One‐Sample Rank Tests -- 14.5 Two‐Sample Rank Tests -- 14.6 Kruskal-Wallis Test -- Chapter 15 Analysis of Categorical Data -- 15.1 Introduction -- 15.2 Chi‐Square Tests -- 15.3 Homogeneity and Independence -- 15.4 Consistency and Power -- 15.5 2 × 2 Contingency Tables -- 15.6 r×c Contingency Tables -- Chapter 16 Basics of Bayesian Statistics -- 16.1 Introduction -- 16.2 Prior and Posterior Distributions -- 16.3 Bayesian Inference -- Predictive Distribution -- Point Estimation -- Bayesian Intervals -- Bayesian Hypotheses Testing -- 16.4 Final Comments -- Appendix A Supporting R Code -- Appendix B Statistical Tables -- Bibliography -- Answers to Odd‐Numbered Problems -- Index -- EULA. |
| Record Nr. | UNINA-9910830705603321 |
Bartoszynski Robert
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probability and statistical inference / / Robert Bartoszynski, Magdalena Niewiadomska-Bugaj
| Probability and statistical inference / / Robert Bartoszynski, Magdalena Niewiadomska-Bugaj |
| Autore | Bartoszyński Robert |
| Edizione | [3rd ed.] |
| Pubbl/distr/stampa | Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2021] |
| Descrizione fisica | 1 online resource (595 pages) |
| Disciplina | 519.54 |
| Collana | Wiley Series in Probability and Statistics Ser. |
| Soggetto topico | Probabilities |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-119-24381-5
1-119-24382-3 1-119-24383-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- Preface to Third Edition -- Preface to Second Edition -- About the Companion Website -- Chapter 1 Experiments, Sample Spaces, and Events -- 1.1 Introduction -- 1.2 Sample Space -- 1.3 Algebra of Events -- 1.4 Infinite Operations on Events -- Chapter 2 Probability -- 2.1 Introduction -- 2.2 Probability as a Frequency -- 2.3 Axioms of Probability -- 2.4 Consequences of the Axioms -- 2.5 Classical Probability -- 2.6 Necessity of the Axioms* -- 2.7 Subjective Probability* -- Chapter 3 Counting -- 3.1 Introduction -- 3.2 Product Sets, Orderings, and Permutations -- 3.3 Binomial Coefficients -- 3.4 Multinomial Coefficients -- Chapter 4 Conditional Probability, Independence, and Markov Chains -- 4.1 Introduction -- 4.2 Conditional Probability -- 4.3 Partitions -- Total Probability Formula -- 4.4 Bayes' Formula -- 4.5 Independence -- 4.6 Exchangeability -- Conditional Independence -- 4.7 Markov Chains* -- Chapter 5 Random Variables: Univariate Case -- 5.1 Introduction -- 5.2 Distributions of Random Variables -- 5.3 Discrete and Continuous Random Variables -- 5.4 Functions of Random Variables -- 5.5 Survival and Hazard Functions -- Chapter 6 Random Variables: Multivariate Case -- 6.1 Bivariate Distributions -- 6.2 Marginal Distributions -- Independence -- 6.3 Conditional Distributions -- 6.4 Bivariate Transformations -- 6.5 Multidimensional Distributions -- Chapter 7 Expectation -- 7.1 Introduction -- 7.2 Expected Value -- 7.3 Expectation as an Integral* -- Riemann Integral -- Lebesque Integral -- Riemann-Stieltjes Integral -- Lebesque-Stieltjes Integral -- Lebesque Integral: General Case -- 7.4 Properties of Expectation -- 7.5 Moments -- 7.6 Variance -- 7.7 Conditional Expectation -- 7.8 Inequalities -- Chapter 8 Selected Families of Distributions -- 8.1 Bernoulli Trials and Related Distributions.
Binomial Distribution -- Geometric Distribution -- Negative Binomial Distribution -- 8.2 Hypergeometric Distribution -- 8.3 Poisson Distribution and Poisson Process -- 8.4 Exponential, Gamma, and Related Distributions -- 8.5 Normal Distribution -- 8.6 Beta Distribution -- Chapter 9 Random Samples -- 9.1 Statistics and Sampling Distributions -- 9.2 Distributions Related to Normal -- 9.3 Order Statistics -- 9.4 Generating Random Samples -- 9.5 Convergence -- Weak Laws of Large Numbers -- Strong Laws of Large Numbers -- 9.6 Central Limit Theorem -- Chapter 10 Introduction to Statistical Inference -- 10.1 Overview -- 10.2 Basic Models -- 10.3 Sampling -- 10.4 Measurement Scales -- Chapter 11 Estimation -- 11.1 Introduction -- 11.2 Consistency -- 11.3 Loss, Risk, and Admissibility -- 11.4 Efficiency -- 11.5 Methods of Obtaining Estimators -- Method of Moments Estimators -- Maximum Likelihood Estimators -- Least Squares Estimators -- Robust Estimators -- 11.6 Sufficiency -- 11.7 Interval Estimation -- Confidence Intervals -- Bootstrap Intervals -- Chapter 12 Testing Statistical Hypotheses -- 12.1 Introduction -- 12.2 Intuitive Background -- 12.3 Most Powerful Tests -- 12.4 Uniformly Most Powerful Tests -- 12.5 Unbiased Tests -- 12.6 Generalized Likelihood Ratio Tests -- 12.7 Conditional Tests -- 12.8 Tests and Confidence Intervals -- 12.9 Review of Tests for Normal Distributions -- One‐Sample Procedures -- Hypotheses About the Variance, Mean Known -- Hypotheses About the Variance, Mean Unknown -- Two‐Sample Procedures -- Large Sample Tests for Binomial Distribution -- 12.10 Monte Carlo, Bootstrap, and Permutation Tests -- Monte Carlo Tests -- Bootstrap Tests -- Permutation Tests -- Chapter 13 Linear Models -- 13.1 Introduction -- 13.2 Regression of the First and Second Kind -- 13.3 Distributional Assumptions -- 13.4 Linear Regression in the Normal Case. 13.5 Testing Linearity -- 13.6 Prediction -- 13.7 Inverse Regression -- 13.8 BLUE -- 13.9 Regression Toward the Mean -- 13.10 Analysis of Variance -- 13.11 One‐Way Layout -- 13.12 Two‐Way Layout -- 13.13 ANOVA Models with Interaction -- 13.14 Further Extensions -- Chapter 14 Rank Methods -- 14.1 Introduction -- 14.2 Glivenko-Cantelli Theorem -- 14.3 Kolmogorov-Smirnov Tests -- One‐Sample Kolmogorov-Smirnov Test -- Two‐Sample Kolmogorov-Smirnov Test -- 14.4 One‐Sample Rank Tests -- 14.5 Two‐Sample Rank Tests -- 14.6 Kruskal-Wallis Test -- Chapter 15 Analysis of Categorical Data -- 15.1 Introduction -- 15.2 Chi‐Square Tests -- 15.3 Homogeneity and Independence -- 15.4 Consistency and Power -- 15.5 2 × 2 Contingency Tables -- 15.6 r×c Contingency Tables -- Chapter 16 Basics of Bayesian Statistics -- 16.1 Introduction -- 16.2 Prior and Posterior Distributions -- 16.3 Bayesian Inference -- Predictive Distribution -- Point Estimation -- Bayesian Intervals -- Bayesian Hypotheses Testing -- 16.4 Final Comments -- Appendix A Supporting R Code -- Appendix B Statistical Tables -- Bibliography -- Answers to Odd‐Numbered Problems -- Index -- EULA. |
| Record Nr. | UNINA-9910555091703321 |
|
Bartoszyński Robert
|
||
| Hoboken, New Jersey : , : John Wiley & Sons, Inc., , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probability and statistical inference [[electronic resource] /] / Robert Bartoszyński and Magdalena Niewiadomska-Bugaj
| Probability and statistical inference [[electronic resource] /] / Robert Bartoszyński and Magdalena Niewiadomska-Bugaj |
| Autore | Bartoszyński Robert |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J. ; ; [Chichester], : Wiley-Interscience, c2008 |
| Descrizione fisica | 1 online resource (662 p.) |
| Disciplina |
519
519.54 |
| Altri autori (Persone) | Niewiadomska-BugajMagdalena |
| Soggetto topico |
Probabilities
Mathematical statistics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-20382-3
9786611203825 0-470-19159-7 0-470-19158-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PROBABILITY AND STATISTICAL INFERENCE; CONTENTS; Preface; 1 Experiments, Sample Spaces, and Events; 1.1 Introduction; 1.2 Sample Space; 1.3 Algebra of Events; 1.4 Infinite Operations on Events; 2 Probability; 2.1 Introduction; 2.2 Probability as a Frequency; 2.3 Axioms of Probability; 2.4 Consequences of the Axioms; 2.5 Classical Probability; 2.6 Necessity of the Axioms; 2.7 Subjective Probability; 3 Counting; 3.1 Introduction; 3.2 Product Sets, Orderings, and Permutations; 3.3 Binomial Coefficients; 3.4 Extension of Newton's Formula; 3.5 Multinomial Coefficients; 4 Conditional Probability
Independence4.1 Introduction; 4.2 Conditional Probability; 4.3 Partitions; Total Probability Formula; 4.4 Bayes' Formula; 4.5 Independence; 4.6 Exchangeability; Conditional Independence; 5 Markov Chains; 5.1 Introduction and Basic Definitions; 5.2 Definition of a Markov Chain; 5.3 n-Step Transition Probabilities; 5.4 The Ergodic Theorem; 5.5 Absorption Probabilities; 6 Random Variables: Univariate Case; 6.1 Introduction; 6.2 Distributions of Random Variables; 6.3 Discrete and Continuous Random Variables; 6.4 Functions of Random Variables; 6.5 Survival and Hazard Functions 7 Random Variables: Multivariate Case7.1 Bivariate Distributions; 7.2 Marginal Distributions; Independence; 7.3 Conditional Distributions; 7.4 Bivariate Transformations; 7.5 Multidimensional Distributions; 8 Expectation; 8.1 Introduction; 8.2 Expected Value; 8.3 Expectation as an Integral; 8.4 Properties of Expectation; 8.5 Moments; 8.6 Variance; 8.7 Conditional Expectation; 8.8 Inequalities; 9 Selected Families of Distributions; 9.1 Bernoulli Trials and Related Distributions; 9.2 Hypergeometric Distribution; 9.3 Poisson Distribution and Poisson Process 9.4 Exponential, Gamma and Related Distributions9.5 Normal Distribution; 9.6 Beta Distribution; 10 Random Samples; 10.1 Statistics and their Distributions; 10.2 Distributions Related to Normal; 10.3 Order Statistics; 10.4 Generating Random Samples; 10.5 Convergence; 11.5 Sampling; 10.6 Central Limit Theorem; 11 Introduction to Statistical Inference; 11.1 Overview; 11.2 Descriptive Statistics; 11.3 Basic Model; 11.4 Bayesian Statistics; 11.6 Measurement Scales; 12 Estimation; 12.1 Introduction; 12.2 Consistency; 12.3 Loss, Risk, and Admissibility; 12.4 Efficiency 12.5 Methods of Obtaining Estimators12.6 Sufficiency; 12.7 Interval Estimation; 13 Testing Statistical Hypotheses; 13.1 Introduction; 13.2 Intuitive Background; 13.3 Most Powerful Tests; 13.4 Uniformly Most Powerful Tests; 13.5 Unbiased Tests; 13.6 Generalized Likelihood Ratio Tests; 13.7 Conditional Tests; 13.8 Tests and Confidence Intervals; 13.9 Review of Tests for Normal Distributions; 13.10 Monte Carlo, Bootstrap, and Permutation Tests; 14 Linear Models; 14.1 Introduction; 14.2 Regression of the First and Second Kind; 14.3 Distributional Assumptions 14.4 Linear Regression in the Normal Case |
| Record Nr. | UNINA-9910144709403321 |
|
Bartoszyński Robert
|
||
| Hoboken, N.J. ; ; [Chichester], : Wiley-Interscience, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probability and statistical inference [[electronic resource] /] / Robert Bartoszyński and Magdalena Niewiadomska-Bugaj
| Probability and statistical inference [[electronic resource] /] / Robert Bartoszyński and Magdalena Niewiadomska-Bugaj |
| Autore | Bartoszyński Robert |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J. ; ; [Chichester], : Wiley-Interscience, c2008 |
| Descrizione fisica | 1 online resource (662 p.) |
| Disciplina |
519
519.54 |
| Altri autori (Persone) | Niewiadomska-BugajMagdalena |
| Soggetto topico |
Probabilities
Mathematical statistics |
| ISBN |
1-281-20382-3
9786611203825 0-470-19159-7 0-470-19158-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PROBABILITY AND STATISTICAL INFERENCE; CONTENTS; Preface; 1 Experiments, Sample Spaces, and Events; 1.1 Introduction; 1.2 Sample Space; 1.3 Algebra of Events; 1.4 Infinite Operations on Events; 2 Probability; 2.1 Introduction; 2.2 Probability as a Frequency; 2.3 Axioms of Probability; 2.4 Consequences of the Axioms; 2.5 Classical Probability; 2.6 Necessity of the Axioms; 2.7 Subjective Probability; 3 Counting; 3.1 Introduction; 3.2 Product Sets, Orderings, and Permutations; 3.3 Binomial Coefficients; 3.4 Extension of Newton's Formula; 3.5 Multinomial Coefficients; 4 Conditional Probability
Independence4.1 Introduction; 4.2 Conditional Probability; 4.3 Partitions; Total Probability Formula; 4.4 Bayes' Formula; 4.5 Independence; 4.6 Exchangeability; Conditional Independence; 5 Markov Chains; 5.1 Introduction and Basic Definitions; 5.2 Definition of a Markov Chain; 5.3 n-Step Transition Probabilities; 5.4 The Ergodic Theorem; 5.5 Absorption Probabilities; 6 Random Variables: Univariate Case; 6.1 Introduction; 6.2 Distributions of Random Variables; 6.3 Discrete and Continuous Random Variables; 6.4 Functions of Random Variables; 6.5 Survival and Hazard Functions 7 Random Variables: Multivariate Case7.1 Bivariate Distributions; 7.2 Marginal Distributions; Independence; 7.3 Conditional Distributions; 7.4 Bivariate Transformations; 7.5 Multidimensional Distributions; 8 Expectation; 8.1 Introduction; 8.2 Expected Value; 8.3 Expectation as an Integral; 8.4 Properties of Expectation; 8.5 Moments; 8.6 Variance; 8.7 Conditional Expectation; 8.8 Inequalities; 9 Selected Families of Distributions; 9.1 Bernoulli Trials and Related Distributions; 9.2 Hypergeometric Distribution; 9.3 Poisson Distribution and Poisson Process 9.4 Exponential, Gamma and Related Distributions9.5 Normal Distribution; 9.6 Beta Distribution; 10 Random Samples; 10.1 Statistics and their Distributions; 10.2 Distributions Related to Normal; 10.3 Order Statistics; 10.4 Generating Random Samples; 10.5 Convergence; 11.5 Sampling; 10.6 Central Limit Theorem; 11 Introduction to Statistical Inference; 11.1 Overview; 11.2 Descriptive Statistics; 11.3 Basic Model; 11.4 Bayesian Statistics; 11.6 Measurement Scales; 12 Estimation; 12.1 Introduction; 12.2 Consistency; 12.3 Loss, Risk, and Admissibility; 12.4 Efficiency 12.5 Methods of Obtaining Estimators12.6 Sufficiency; 12.7 Interval Estimation; 13 Testing Statistical Hypotheses; 13.1 Introduction; 13.2 Intuitive Background; 13.3 Most Powerful Tests; 13.4 Uniformly Most Powerful Tests; 13.5 Unbiased Tests; 13.6 Generalized Likelihood Ratio Tests; 13.7 Conditional Tests; 13.8 Tests and Confidence Intervals; 13.9 Review of Tests for Normal Distributions; 13.10 Monte Carlo, Bootstrap, and Permutation Tests; 14 Linear Models; 14.1 Introduction; 14.2 Regression of the First and Second Kind; 14.3 Distributional Assumptions 14.4 Linear Regression in the Normal Case |
| Record Nr. | UNINA-9910830523803321 |
|
Bartoszyński Robert
|
||
| Hoboken, N.J. ; ; [Chichester], : Wiley-Interscience, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Probability and statistical inference [[electronic resource] /] / Robert Bartoszyński and Magdalena Niewiadomska-Bugaj
| Probability and statistical inference [[electronic resource] /] / Robert Bartoszyński and Magdalena Niewiadomska-Bugaj |
| Autore | Bartoszyński Robert |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Hoboken, N.J. ; ; [Chichester], : Wiley-Interscience, c2008 |
| Descrizione fisica | 1 online resource (662 p.) |
| Disciplina |
519
519.54 |
| Altri autori (Persone) | Niewiadomska-BugajMagdalena |
| Soggetto topico |
Probabilities
Mathematical statistics |
| ISBN |
1-281-20382-3
9786611203825 0-470-19159-7 0-470-19158-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
PROBABILITY AND STATISTICAL INFERENCE; CONTENTS; Preface; 1 Experiments, Sample Spaces, and Events; 1.1 Introduction; 1.2 Sample Space; 1.3 Algebra of Events; 1.4 Infinite Operations on Events; 2 Probability; 2.1 Introduction; 2.2 Probability as a Frequency; 2.3 Axioms of Probability; 2.4 Consequences of the Axioms; 2.5 Classical Probability; 2.6 Necessity of the Axioms; 2.7 Subjective Probability; 3 Counting; 3.1 Introduction; 3.2 Product Sets, Orderings, and Permutations; 3.3 Binomial Coefficients; 3.4 Extension of Newton's Formula; 3.5 Multinomial Coefficients; 4 Conditional Probability
Independence4.1 Introduction; 4.2 Conditional Probability; 4.3 Partitions; Total Probability Formula; 4.4 Bayes' Formula; 4.5 Independence; 4.6 Exchangeability; Conditional Independence; 5 Markov Chains; 5.1 Introduction and Basic Definitions; 5.2 Definition of a Markov Chain; 5.3 n-Step Transition Probabilities; 5.4 The Ergodic Theorem; 5.5 Absorption Probabilities; 6 Random Variables: Univariate Case; 6.1 Introduction; 6.2 Distributions of Random Variables; 6.3 Discrete and Continuous Random Variables; 6.4 Functions of Random Variables; 6.5 Survival and Hazard Functions 7 Random Variables: Multivariate Case7.1 Bivariate Distributions; 7.2 Marginal Distributions; Independence; 7.3 Conditional Distributions; 7.4 Bivariate Transformations; 7.5 Multidimensional Distributions; 8 Expectation; 8.1 Introduction; 8.2 Expected Value; 8.3 Expectation as an Integral; 8.4 Properties of Expectation; 8.5 Moments; 8.6 Variance; 8.7 Conditional Expectation; 8.8 Inequalities; 9 Selected Families of Distributions; 9.1 Bernoulli Trials and Related Distributions; 9.2 Hypergeometric Distribution; 9.3 Poisson Distribution and Poisson Process 9.4 Exponential, Gamma and Related Distributions9.5 Normal Distribution; 9.6 Beta Distribution; 10 Random Samples; 10.1 Statistics and their Distributions; 10.2 Distributions Related to Normal; 10.3 Order Statistics; 10.4 Generating Random Samples; 10.5 Convergence; 11.5 Sampling; 10.6 Central Limit Theorem; 11 Introduction to Statistical Inference; 11.1 Overview; 11.2 Descriptive Statistics; 11.3 Basic Model; 11.4 Bayesian Statistics; 11.6 Measurement Scales; 12 Estimation; 12.1 Introduction; 12.2 Consistency; 12.3 Loss, Risk, and Admissibility; 12.4 Efficiency 12.5 Methods of Obtaining Estimators12.6 Sufficiency; 12.7 Interval Estimation; 13 Testing Statistical Hypotheses; 13.1 Introduction; 13.2 Intuitive Background; 13.3 Most Powerful Tests; 13.4 Uniformly Most Powerful Tests; 13.5 Unbiased Tests; 13.6 Generalized Likelihood Ratio Tests; 13.7 Conditional Tests; 13.8 Tests and Confidence Intervals; 13.9 Review of Tests for Normal Distributions; 13.10 Monte Carlo, Bootstrap, and Permutation Tests; 14 Linear Models; 14.1 Introduction; 14.2 Regression of the First and Second Kind; 14.3 Distributional Assumptions 14.4 Linear Regression in the Normal Case |
| Record Nr. | UNINA-9910840841103321 |
|
Bartoszyński Robert
|
||
| Hoboken, N.J. ; ; [Chichester], : Wiley-Interscience, c2008 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||