Mathematical Statistics and Data Analysis
Mathematical Statistics and Data Analysis
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DOI：
10.2307/2291188
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发表时间：
1988-01
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影响因子：
--
通讯作者：
J. Rice
中科院分区：
文献类型：
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作者：
J. Rice
1。概率。介绍。样品空间。概率度量。计算概率：计数方法。有条件的概率。独立。总结说。问题。 2。随机变量。离散的随机变量。连续的随机变量。随机变量的功能。总结说。问题。 3。联合分布。介绍。离散的随机变量。连续的随机变量。独立的随机变量。条件分布。联合分布的随机变量的函数。超级和秩序统计。问题。 4。期望值。随机变量的预期值。方差和标准偏差。协方差和相关性。有条件的期望和预测。力矩生成功能。近似方法。问题。 5。限制定理。介绍。大量定律。分布和中心极限定理的收敛。问题。 6。从正态分布得出的分布。介绍。卡方，T和F分布。样本均值和样本方差。问题。 7。调查抽样。介绍。人口参数。简单的随机抽样。比率的估计。分层随机抽样。总结说。问题。 8。参数的估计和概率分布的拟合。介绍。将泊松分布拟合到α颗粒的排放中。参数估计。时刻的方法。最大似然的方法。参数估计的贝叶斯方法。效率和Cramer-Rao下限。足够。总结说。问题。 9。测试假设并评估拟合良好。介绍。 Neyman-Pearson范式。置信区间和假设检验的双重性。普遍的似然比测试。多项式分布的似然比测试。泊松分散测试。悬挂的根部图。概率图。测试正态性。总结说。问题。 10。总结数据。介绍。基于累积分布函数的方法。直方图，密度曲线和茎叶图。位置度量。分散措施。箱形图。探索与散点图的关系。总结说。问题。 11。比较两个样本。介绍。比较两个独立的样本。比较配对样品。实验设计。总结说。问题。 12。方差分析。介绍。单向布局。双向布局。总结说。问题。 13。分类数据的分析。介绍。 Fisher的精确测试。同质性的卡方检验。卡方独立性。匹配对双设计。赔率比。结论备注。问题。14。线性最小二乘。简介。简介。简单的线性回归。矩阵方法。最小二乘统计特性。 Bootstrap索引。
1. PROBABILITY. Introduction. Sample Spaces. Probability Measures. Computing Probabilities: Counting Methods. Conditional Probability. Independence. Concluding Remarks. Problems. 2. RANDOM VARIABLES. Discrete Random Variables. Continuous Random Variables. Functions of a Random Variable. Concluding Remarks. Problems. 3. JOINT DISTRIBUTIONS. Introduction. Discrete Random Variables. Continuous Random Variables. Independent Random Variables. Conditional Distributions. Functions of Jointly Distributed Random Variables. Extrema and Order Statistics. Problems. 4. EXPECTED VALUES. The Expected Value of a Random Variable. Variance and Standard Deviation. Covariance and Correlation. Conditional Expectation and Prediction. The Moment-Generating Function. Approximate Methods. Problems. 5. LIMIT THEOREMS. Introduction. The Law of Large Numbers. Convergence in Distribution and the Central Limit Theorem. Problems . 6. DISTRIBUTIONS DERIVED FROM THE NORMAL DISTRIBUTION. Introduction. Chi-Squared, t, and F Distributions. The Sample Mean and Sample Variance. Problems. 7. SURVEY SAMPLING. Introduction. Population Parameters. Simple Random Sampling. Estimation of a Ratio. Stratified Random Sampling. Concluding Remarks. Problems. 8. ESTIMATION OF PARAMETERS AND FITTING OF PROBABILITY DISTRIBUTIONS. Introduction. Fitting the Poisson Distribution to the Emissions of Alpha Particles. Parameter Estimation. The Method of Moments. The Method of Maximum Likelihood. The Bayesian Approach to Parameter Estimation. Efficiency and the Cramer-Rao Lower Bound. Sufficiency. Concluding Remarks. Problems. 9. TESTING HYPOTHESES AND ASSESSING GOODNESS OF FIT. Introduction. The Neyman-Pearson Paradigm. The Duality of Confidence Intervals and Hypothesis Tests. Generalized Likelihood Ratio Tests. Likelihood Ratio Tests for the Multinomial Distribution. The Poisson Dispersion Test. Hanging Rootograms. Probability Plots. Tests for Normality. Concluding Remarks. Problems. 10. SUMMARIZING DATA. Introduction. Methods Based on the Cumulative Distribution Function. Histograms, Density Curves, and Stem-and-Leaf Plots. Measures of Location. Measures of Dispersion. Boxplots. Exploring Relationships with Scatterplots. Concluding Remarks. Problems. 11. COMPARING TWO SAMPLES. Introduction. Comparing Two Independent Samples. Comparing Paired Samples. Experimental Design. Concluding Remarks. Problems. 12. THE ANALYSIS OF VARIANCE. Introduction. The One-Way Layout. The Two-Way Layout. Concluding Remarks. Problems. 13. THE ANALYSIS OF CATEGORICAL DATA. Introduction. Fisher"s Exact Test. The Chi-Square Test of Homogeneity. The Chi-Square Test of Independence. Matched-Pairs Designs. Odds Ratios. Concluding Remarks. Problems. 14. LINEAR LEAST SQUARES. Introduction. Simple Linear Regression. The Matrix Approach to Linear Least Squares. Statistical Properties of Least Squares Estimates. Multiple Linear Regression--An Example. Conditional Inference, Unconditional Inference, and the Bootstrap. Concluding Remarks. Problems. 15. DECISION THEORY AND BAYESIAN INFERENCE. Introduction. Decision Theory. The Subjectivist Point of View. Concluding Remarks. Problems. Appendix A. Common Distributions. Appendix B. Tables. Bibliography. Answers to Selected Problems. Author Index. Index to Data Sets. Subject Index.