Examples and problems in mathematical statistics
Shelemyahu Zacks.
Bok Engelsk 2014 · Electronic books.
| Omfang | 1 online resource (654 p.)
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| Utgave | 1st edition
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| Opplysninger | Description based upon print version of record.. - Examples and Problems in Mathematical Statistics; Contents; Preface; List of Random Variables; List of Abbreviations; 1 Basic Probability Theory; PART I: THEORY; 1.1 OPERATIONS ON SETS; 1.2 ALGEBRA AND σ-FIELDS; 1.3 PROBABILITY SPACES; 1.4 CONDITIONAL PROBABILITIES AND INDEPENDENCE; 1.5 RANDOM VARIABLES AND THEIR DISTRIBUTIONS; 1.6 THE LEBESGUE AND STIELTJES INTEGRALS; 1.6.1 General Definition of Expected Value: The Lebesgue Integral; 1.6.2 The Stieltjes-Riemann Integral; 1.6.3 Mixtures of Discrete and Absolutely Continuous Distributions; 1.6.4 Quantiles of Distributions. - 1.13.6 The Empirical Distribution and Sample QuantilesPART II: EXAMPLES; PART III: PROBLEMS; PART IV: SOLUTIONS TO SELECTED PROBLEMS; 2 Statistical Distributions; PART I: THEORY; 2.1 INTRODUCTORY REMARKS; 2.2 FAMILIES OF DISCRETE DISTRIBUTIONS; 2.2.1 Binomial Distributions; 2.2.2 Hypergeometric Distributions; 2.2.3 Poisson Distributions; 2.2.4 Geometric, Pascal, and Negative Binomial Distributions; 2.3 SOME FAMILIES OF CONTINUOUS DISTRIBUTIONS; 2.3.1 Rectangular Distributions; 2.3.2 Beta Distributions; 2.3.3 Gamma Distributions; 2.3.4 Weibull and Extreme Value Distributions. - 1.6.5 Transformations1.7 JOINT DISTRIBUTIONS, CONDITIONAL DISTRIBUTIONS AND INDEPENDENCE; 1.7.1 Joint Distributions; 1.7.2 Conditional Expectations: General Definition; 1.7.3 Independence; 1.8 MOMENTS AND RELATED FUNCTIONALS; 1.9 MODES OF CONVERGENCE; 1.10 WEAK CONVERGENCE; 1.11 LAWS OF LARGE NUMBERS; 1.11.1 The Weak Law of Large Numbers (WLLN); 1.11.2 The Strong Law of Large Numbers (SLLN); 1.12 CENTRAL LIMIT THEOREM; 1.13 MISCELLANEOUS RESULTS; 1.13.1 Law of the Iterated Logarithm; 1.13.2 Uniform Integrability; 1.13.3 Inequalities; 1.13.4 The Delta Method; 1.13.5 The Symbols op and Op. - 2.3.5 Normal Distributions2.3.6 Normal Approximations; 2.4 TRANSFORMATIONS; 2.4.1 One-to-One Transformations of Several Variables; 2.4.2 Distribution of Sums; 2.4.3 Distribution of Ratios; 2.5 VARIANCES AND COVARIANCES OF SAMPLE MOMENTS; 2.6 DISCRETE MULTIVARIATE DISTRIBUTIONS; 2.6.1 The Multinomial Distribution; 2.6.2 Multivariate Negative Binomial; 2.6.3 Multivariate Hypergeometric Distributions; 2.7 MULTINORMAL DISTRIBUTIONS; 2.7.1 Basic Theory; 2.7.2 Distribution of Subvectors and Distributions of Linear Forms; 2.7.3 Independence of Linear Forms. - 2.8 DISTRIBUTIONS OF SYMMETRIC QUADRATIC FORMS OF NORMAL VARIABLES2.9 INDEPENDENCE OF LINEAR AND QUADRATIC FORMS OF NORMAL VARIABLES; 2.10 THE ORDER STATISTICS; 2.11 t-DISTRIBUTIONS; 2.12 F-DISTRIBUTIONS; 2.13 THE DISTRIBUTION OF THE SAMPLE CORRELATION; 2.14 EXPONENTIAL TYPE FAMILIES; 2.15 APPROXIMATING THE DISTRIBUTION OF THE SAMPLE MEAN: EDGEWORTH AND SADDLEPOINT APPROXIMATIONS; 2.15.1 Edgeworth Expansion; 2.15.2 Saddlepoint Approximation; PART II: EXAMPLES; PART III: PROBLEMS; PART IV: SOLUTIONS TO SELECTED PROBLEMS; 3 Sufficient Statistics and the Information in Samples; PART I: THEORY. - 3.1 INTRODUCTION. - "This book presents examples that illustrate the theory of mathematical statistics and details how to apply the methods for solving problems"--
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| Emner | |
| Sjanger | |
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| ISBN | 1-118-60583-7. - 1-118-60600-0
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| Hylleplass | QA276 .Z265 2014
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