Front Cover -- Statistical Methods in the Atmospheric Sciences -- Copyright Page -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- PART I: Preliminaries -- CHAPTER 1. Introduction -- 1.1 What Is Statistics? -- 1.2 Descriptive and Inferential Statistics -- 1.3 Uncertainty about the Atmosphere -- CHAPTER 2. Review of Probability -- 2.1 Background -- 2.2 The Elements of Probability -- 2.3 The Meaning of Probability -- 2.4 Some Properties of Probability -- 2.5 Exercises -- PART II: Univariate Statistics -- CHAPTER 3. Empirical Distributions and Exploratory Data Analysis -- 3.1 Background -- 3.2 Numerical Summary Measures -- 3.3 Graphical Summary Techniques -- 3.4 Reexpression -- 3.5 Exploratory Techniques for Paired Data -- 3.6 Exploratory Techniques for Higher-Dimensional Data -- 3.7 Exercises -- CHAPTER 4. Parametric Probability Distributions -- 4.1 Background -- 4.2 Discrete Distributions -- 4.3 Statistical Expectations -- 4.4 Continuous Distributions -- 4.5 Qualitative Assessments of the Goodness of Fit -- 4.6 Parameter Fitting Using Maximum Likelihood -- 4.7 Statistical Simulation -- 4.8 Exercises -- CHAPTER 5. Hypothesis Testing -- 5.1 Background -- 5.2 Some Parametric Tests -- 5.3 Nonparametric Tests -- 5.4 Field Significance and Multiplicity -- 5.5 Exercises -- CHAPTER 6. Statistical Forecasting -- 6.1 Background -- 6.2 Linear Regression -- 6.3 Nonlinear Regression -- 6.4 Predictor Selection -- 6.5 Objective Forecasts Using Traditional Statistical Methods -- 6.6 Ensemble Forecasting -- 6.7 Subjective Probability Forecasts -- 6.8 Exercises -- CHAPTER 7. Forecast Verification -- 7.1 Background -- 7.2 Nonprobabilistic Forecasts of Discrete Predictands -- 7.3 Nonprobabilistic Forecasts of Continuous Predictands.

7.4 Probability Forecasts of Discrete Predictands -- 7.5 Probability Forecasts for Continuous Predictands -- 7.6 Nonprobabilistic Forecasts of Fields -- 7.7 Verification of Ensemble Forecasts -- 7.8 Verification Based on Economic Value -- 7.9 Sampling and Inference for Verification Statistics -- 7.10 Exercises -- CHAPTER 8. Time Series -- 8.1 Background -- 8.2 Time Domain-I. Discrete Data -- 8.3 Time Domain-II. Continuous Data -- 8.4 Frequency Domain-I. Harmonic Analysis -- 8.5 Frequency Domain-II. Spectral Analysis -- 8.6 Exercises -- PART III: Multivariate Statistics -- CHAPTER 9. Matrix Algebra and Random Matrices -- 9.1 Background to Multivariate Statistics -- 9.2 Multivariate Distance -- 9.3 Matrix Algebra Review -- 9.4 Random Vectors and Matrices -- 9.5 Exercises -- CHAPTER 10. The Multivariate Normal (MVN) Distribution -- 10.1 Definition of the MVN -- 10.2 Four Handy Properties of the MVN -- 10.3 Assessing Multinormality -- 10.4 Simulation from the Multivariate Normal Distribution -- 10.5 Inferences about a Multinormal Mean Vector -- 10.6 Exercises -- CHAPTER 11. Principal Component (EOF) Analysis -- 11.1 Basics of Principal Component Analysis -- 11.2 Application of PCA to Geophysical Fields -- 11.3 Truncation of the Principal Components -- 11.4 Sampling Properties of the Eigenvalues and Eigenvectors -- 11.5 Rotation of the Eigenvectors -- 11.6 Computational Considerations -- 11.7 Some Additional Uses of PCA -- 11.8 Exercises -- CHAPTER 12. Canonical Correlation Analysis (CCA) -- 12.1 Basics of CCA -- 12.2 CCA Applied to Fields -- 12.3 Computational Considerations -- 12.4 Maximum Covariance Analysis -- 12.5 Exercises -- CHAPTER 13. Discrimination and Classification -- 13.1 Discrimination vs. Classification -- 13.2 Separating Two Populations -- 13.3 Multiple Discriminant Analysis (MDA).

13.4 Forecasting with Discriminant Analysis -- 13.5 Alternatives to Classical Discriminant Analysis -- 13.6 Exercises -- CHAPTER 14. Cluster Analysis -- 14.1 Background -- 14.2 Hierarchical Clustering -- 14.3 Nonhierarchical Clustering -- 14.4 Exercises -- APPENDIX A. Example Data Sets -- Table A.1. Daily precipitation and temperature data for Ithaca and Canandaigua, New York, for January 1987 -- Table A.2. January precipitation data for Ithaca, New York, 1933-1982 -- Table A.3. June climate data for Guayaquil, Ecuador, 1951-1970 -- APPENDIX B. Probability Tables -- Table B.1. Cumulative Probabilities for the Standard Gaussian Distribution -- Table B.2. Quantiles of the Standard Gamma Distribution -- Table B.3. Right-tail quantiles of the Chi-square distribution -- APPENDIX C. Answers to Exercises -- References -- Index.