Multivariate Analysis

  1. The Multivariate Normal Distribution
    1. Bivariate Normal Distribution
      1. Joint Density Function
        1. Marginal Distributions
          1. Conditional Distributions
            1. Correlation Parameter
              1. Geometric Properties
              2. Multivariate Normal Density Function
                1. General Formulation
                  1. Parameters
                    1. Mean Vector
                      1. Covariance Matrix
                      2. Standardized Form
                      3. Properties of Multivariate Normal Distribution
                        1. Linear Combinations
                          1. Marginal Distributions
                            1. Conditional Distributions
                              1. Independence and Correlation
                                1. Quadratic Forms
                                2. Sampling from Multivariate Normal Distribution
                                  1. Random Vector Generation
                                    1. Simulation Methods
                                    2. Assessing Multivariate Normality
                                      1. Univariate Normality Assessment
                                        1. Histograms
                                          1. Q-Q Plots
                                            1. Shapiro-Wilk Test
                                            2. Bivariate Assessment
                                              1. Scatter Plots
                                                1. Elliptical Patterns
                                                2. Multivariate Normality Tests
                                                  1. Mardia's Test
                                                    1. Henze-Zirkler Test
                                                      1. Royston's Test
                                                        1. Energy Test
                                                      2. Transformations to Achieve Normality
                                                        1. Logarithmic Transformation
                                                          1. Box-Cox Transformation
                                                            1. Yeo-Johnson Transformation
                                                              1. Rank-Based Transformations

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                                                            4. Data Preparation and Exploration