An Introduction to Probability and Statistical Inference (2版)

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統計推論(casella: statistical inference 2/e) (2版)

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【簡介】 作者以理論性的概念方式有系統地介紹並證明機率理論與統計理論；首先是深入淺出且完整地闡述機率概念、基本性質以及機率分配的特性，藉以應用在後續的統計理論的理論驗證問題，清楚地分析與分類統計方法的概念、驗證過程、特性，以及使用時機。 同時，對各統計方法的相互因果關係，也有明白地驗證。此書以統計推論為名，已明確指出統計理論為其主要內容，而統計推論的理論基礎為機率理論，可知此書仍不脫離一般理論統計或數理統計書籍的輪廓，機率的章節只是為主要內容舖路。因此，此書雖以統計推論為名，實與高等統計、理論統計、數理統計、統計理論的課程教材相通。 【目錄】 第1章　機率理論 第2章　變數變換與期望值 第3章　常用的分配 第4章　多元隨機變數 第5章　隨機樣本的特性 第6章　資料縮減的原理 第7章　點估計 第8章　假設檢定 第9章　區間估計 第10章　漸近評量法 第11章　變異數分析與迴歸的分析 第12章　迴歸模型

STATISTICAL INFERENCE 2/e (2版)

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【原文書】 書名：Statistical Inference 2/E 作者：George Casella 出版社：CENGAGE ISBN：9780534243128 Table of contents 1. Probability Theory. Set Theory. Probability Theory. Conditional Probability and Independence. Random Variables. Distribution Functions. Density and Mass Functions. Exercises. Miscellanea. 2. Transformations and Expectations. Distribution of Functions of a Random Variable. Expected Values. Moments and Moment Generating Functions. Differentiating Under an Integral Sign. Exercises. Miscellanea. 3. Common Families of Distributions. Introductions. Discrete Distributions. Continuous Distributions. Exponential Families. Locations and Scale Families. Inequalities and Identities. Exercises. Miscellanea. 4. Multiple Random Variables. Joint and Marginal Distributions. Conditional Distributions and Independence. Bivariate Transformations. Hierarchical Models and Mixture Distributions. Covariance and Correlation. Multivariate Distributions. Inequalities. Exercises. Miscellanea. 5. Properties of a Random Sample. Basic Concepts of Random Samples. Sums of Random Variables from a Random Sample. Sampling for the Normal Distribution. Order Statistics. Convergence Concepts. Generating a Random Sample. Exercises. Miscellanea. 6. Principles of Data Reduction. Introduction. The Sufficiency Principle. The Likelihood Principle. The Equivariance Principle. Exercises. Miscellanea. 7. Point Estimation. Introduction. Methods of Finding Estimators. Methods of Evaluating Estimators. Exercises. Miscellanea. 8. Hypothesis Testing. Introduction. Methods of Finding Tests. Methods of Evaluating Test. Exercises. Miscellanea. 9. Interval Estimation. Introduction. Methods of Finding Interval Estimators. Methods of Evaluating Interval Estimators. Exercises. Miscellanea. 10. Asymptotic Evaluations. Point Estimation. Robustness. Hypothesis Testing. Interval Estimation. Exercises. Miscellanea. 11. Analysis of Variance and Regression. Introduction. One-way Analysis of Variance. Simple Linear Regression. Exercises. Miscellanea. 12. Regression Models. Introduction. Regression with Errors in Variables. Logistic Regression. Robust Regression. Exercises. Miscellanea. Appendix. Computer Algebra. References.