Sampling | CDFs | Empirical CDF | Lower Partial Moment CDF (LPM.ratio) | LPM.ratio degree > 0 | Generating PDFs with (LPM.VaR) | Simulation | Bootstrapping (NNS.meboot) | target_drift Specification | Simulating a Multivariate Dependence Structure | Compare Multivariate Dependence Structures | Alternative Using NNS.meboot | References

Orientation | 1. Foundations — Partial Moments & Variance Decomposition | 1.1 Why partial moments | 1.2 Core functions and headers | 1.3 Code: variance decomposition & CDF | 2. Descriptive & Distributional Tools | 2.1 Higher moments from partial moments | 2.2 Mode estimation (no bin‑or‑bandwidth angst) | 2.3 CDF tables via LPM ratios | 3. Dependence & Nonlinear Association | 3.1 Why move beyond Pearson (r) | 3.2 Code: nonlinear dependence | 3.3 Code: copula | 4. Normalization and Rescaling | 4.1 Normalization | 4.2 Risk‑neutral rescale (pricing context) | 5. Hypothesis Testing, ANOVA & Stochastic Superiority | 5.1 Concept | 5.2 Code: two‑sample & multi‑group | 5.3 Stochastic Superiority | 6. Regression, Boosting, Stacking & Causality | 6.1 Philosophy | 6.2 Code: classification via regression + ensembles | 6.3 Code: directional causality | 7. Time Series & Forecasting | 8. Simulation & Bootstrap & Risk‑Neutral Rescaling | 8.1 Maximum entropy bootstrap (shape‑preserving) | 8.2 Monte Carlo over the full correlation space | 9. Portfolio & Stochastic Dominance | Appendix A — Measure‑theoretic sketch (why partial moments are rigorous) | Appendix B — Quick Reference (Grouped by Topic) | Overall Theory | 1. Partial Moments & Ratios | 2. Descriptive Statistics & Distributions | 3. Dependence & Association | 4. Normalization & Rescaling | 5. Hypothesis Testing | 6. Regression, Classification & Causality | 7. Differentiation & Slope Measures | 8. Time Series & Forecasting | 9. Simulation & Bootstrap | 10. Portfolio Analysis & Stochastic Dominance

Partial Moments | Mean | Variance | Standard Deviation | First 4 Moments | Statistical Mode of a Continuous Distribution | Covariance | Covariance Elements and Covariance Matrix | Pearson Correlation | CDFs (Discrete and Continuous) | Numerical Integration | Bayes' Theorem | References

Correlation and Dependence | Linear Equivalence | Nonlinear Relationship | Cyclic Relationship | Asymmetrical Analysis | Dependence | p-values for NNS.dep() | Multivariate Dependence NNS.copula() | References

Overview | NNS.norm(): Normalize Multiple Variables | Mathematical Structure | Step 1: Compute Mean Vector | Step 2: Construct Mean Ratio Matrix | Step 3: Dependence Weight Matrix | Step 4: Scaling Factors | Linear Case Proof | Nonlinear Case Interpretation | [\text{mean}(X_{\cdot j}^{*}) | Examples | Basic Multivariate Example | Normalize list of unequal vector lengths | Quantile Normalization Comparison | Practical Applications | NNS.rescale(): Distribution Rescaling | 1) Min-Max Scaling | [x^ | Example | 2) Risk-Neutral Scaling | Terminal Type | Discounted Type | Risk-Neutral Example | Discounted Example | Conceptual Summary | NNS.norm() | NNS.rescale() | References

Comparing Distributions | Test if Same Population | Test if means are Equal | Test if means are Unequal | Medians | Stochastic Superiority | Stochastic Dominance | Stochastic Dominant Efficient Sets | Stochastic Dominant Clusters | References

Clustering and Regression | NNS Partitioning NNS.part() | X-only Partitioning | Clusters Used in Regression | NNS Regression NNS.reg() | Univariate: | Multivariate: | Inter/Extrapolation | NNS Dimension Reduction Regression | Threshold | Classification | Cross-Validation NNS.stack() | Increasing Dimensions | Smoothing Option | Imputation | Univariate Imputation | Multivariate Imputation | A Note on Uncertainty Propagation | References

Classification | Splits vs. Partitions | NNS Partitions | NNS.boost() | Cross-Validation Classification Using NNS.stack() | Brief Notes on Other Parameters | References

Forecasting | Linear Regression | Nonlinear Regression | Cross-Validation | Cross-Validating All Combinations of seasonal.factor | Extension of Estimates | Brief Notes on Other Parameters | Multivariate Time Series Forecasting | References