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Mathematical theory of probability and statistics
Mathematical Theory of Probability and Statistics.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1964.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Mathematical Theory of Probability and Statistics; Copyright Page; PREFACE; Table of Contents; CHAPTERI. FUNDAMENTALS; A. The Basic Assumptions (Sections 1-5); B. The Operations (Sections 6-10); APPENDIX ONE : THE CONSISTENCY OF THE NOTION OF THE COLLECTIVE. WALD'S RESULTS; APPENDIX TWO: MEASURE-THEORETICAL APPROACH VERSUS FREQUENCY APPROACH; CHAPTERII. GENERAL LABEL SPACE; A. Distribution Function (Discrete Case). Measure-Theoretical Approach (Sections 1-3); B. Non-Countable Label Space. Frequency Approach (Sections 4-7); APPENDIX THREE: TORNIER'S FREQUENCY THEORY.
- CHAPTERIII. BASIC PROPERTIES OF DISTRIBUTIONSA. Mean Value, Variance, and Other Moments (Sections 1-4); B. Gaussian Distribution, Poisson Distribution (Sections 5 and 6); C. Distributions in Rn (Sections 7 and 8); CHAPTERIV. EXAMPLES OF COMBINED OPERATIONS; A. Uniform Distributions (Sections 1 and 2); B. Bernoulli Problem and Related Questions (Sections 3-6); C. Some Problems of Non-independent Events (Sections 7-9); D. Application to Mendelian Heredity Theory (Sections 10 and 11); E. Comments On Markov Chains (Sections 12 and 13).
- CHAPTERV. SUMMATION OF CHANCE VARIABLES CHARACTERISTIC FUNCTIONA. Summation of Chance Variables and Laws of Large Numbers (Sections 1-4); B. Characteristic Function (Sections 5-8); CHAPTERVI. ASYMPTOTIC DISTRIBUTION OF THE SUM OF CHANCE VARIABLES; A. Asymptotic Results for Infinite Products. Stirling's Formula. Laplace's Formula (Sections 1 and 2); B. Limit Distribution of the Sum of Independent Discrete Random Variables (Sections 3 and 4); C. Probability Density. Central Limit Theorem. Lindeberg's and Liapounoff's Conditions (Sections 5-7).
- D. Probability of the Sum of Rare Events. Compound Poisson Distribution (Sections 8-10)APPENDIX FOUR : REMARKS ON ADDITIVETIME-DEPENDENT STOCHASTIC PROCESSES; CHAPTERVII. PROBABILITY INFERENCE. BAYES' METHOD; A. Inference from a Finite Number of Observations (Sections1-2); B. Law of Large Numbers (Section 3); C. Asymptotic Distributions (Sections 4-6); D. Rare Events (Section 7); CHAPTERVIII. MORE ON DISTRIBUTIONS; A. Sample Distribution and Statistical Parameters (Section 1-3); B. Moments. Inequalities (Sections 4 and 5).
- C. Various Distributions Related to Normal Distributions (Sections 6 and 7)D. Multivariate Normal Distribution (Sections 8 and 9); CHAPTERIX. ANALYSIS OF STATISTICAL DATA; A. Lexis Theory (Sections 1 and 2); B. Student Test and F-Test (Section 3); C. The X2-Test (Sections 4 and 5); D. Thew2-Tests (Sections 6 and 7); E. Deviation Tests (Section 8); CHAPTERX. PROBLEM OF INFERENCE; A. Testing Hypotheses (Sections 1-4); B. Global Statements on Parameters (Section 5); C. Estimation (Sections 6 and 7); CHAPTERXI. MULTIVARIATE STATISTICS. CORRELATION; A. Measures of Correlation in Two Dimensions (Sections 1-3).