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Essential Statistics for Quant Finance

Quantitative finance relies heavily on statistics to analyze data, model risk, and make predictions. Here are the core statistics topics and modules you should master:

1. Descriptive Statistics

Mean, median, mode
Variance, standard deviation
Skewness, kurtosis
Data visualization (histograms, box plots)

2. Probability Theory

Probability distributions (normal, lognormal, binomial, Poisson, etc.)
Random variables
Expectation, variance
Law of large numbers, central limit theorem

3. Statistical Inference

Sampling methods
Estimation (point, interval)
Hypothesis testing
p-values, confidence intervals

4. Regression Analysis

Simple and multiple linear regression
Logistic regression
Residual analysis
Model selection and diagnostics

5. Time Series Analysis

Stationarity
Autocorrelation, partial autocorrelation
AR, MA, ARMA, ARIMA models
Volatility modeling (GARCH)
Forecasting

6. Multivariate Statistics

Covariance and correlation matrices
Principal component analysis (PCA)
Factor models
Dimensionality reduction

7. Bayesian Statistics

Bayes’ theorem
Prior, likelihood, posterior
Bayesian inference and updating

8. Nonparametric Methods

Rank-based tests
Kernel density estimation
Bootstrap methods

9. Machine Learning & Statistical Learning

Supervised and unsupervised learning
Classification, regression, clustering
Overfitting, cross-validation
Feature selection

10. Risk and Performance Metrics

Value at Risk (VaR)
Expected Shortfall
Sharpe ratio, Sortino ratio
Drawdown analysis

11. Simulation Methods

Monte Carlo simulation
Scenario analysis
Random number generation

12. Optimization

Linear and nonlinear programming
Constrained optimization
Portfolio optimization

Conclusion

Mastering these statistics topics will provide a strong foundation for quantitative finance. Each area builds skills for analyzing financial data, modeling uncertainty, and making informed investment decisions.

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