Statistics

This repository contains notes, explanations, and code snippets covering essential statistics concepts and techniques. Topics range from basic probability and descriptive statistics to more advanced concepts such as hypothesis testing and confidence intervals.

Requirements

The programming examples are implemented in Python for its simplicity, versatility, and rich scientific computing ecosystem. The code makes use of widely used libraries such as:

• NumPy for numerical computing
• SciPy for advanced scientific computations
• pandas for data manipulation and analysis

A basic understanding of Python and its scientific libraries will help you make the most of the code examples.

Setting up your environment

We recommend using a virtual environment to avoid package conflicts.

# Create a virtual environment
python3 -m venv env

Activate the environment:

# On Windows
env\Scripts\activate

# On Unix or macOS
source env/bin/activate

Install the dependencies:

pip install -r requirements.txt

Now you’re ready to run the scripts:

python scripts/basic_concepts/basic_concepts.py

Replace scripts/basic_concepts/basic_concepts.py with the actual path to the script you want to run.

When finished, deactivate the environment:

deactivate

Topics

Basic Concepts

Concept	Notes	Implementation	Examples
Introduction to Statistics
Descriptive Statistics
Introduction to Probability		N/A	N/A
Geometric Probability
Axioms of Probability		N/A	N/A
Conditional Probability and Independence		N/A	N/A
Bayes Theorem
Probability Trees		N/A	N/A
Total Probability		N/A	N/A
Bayesian vs Frequentist

Probability Distributions

Concept	Notes	Implementation	Examples
Introduction to Distributions
Central Limit Theorem
Beta Distribution
Chi-Square Distribution
Exponential Distribution
F Distribution
Gamma Distribution
Log-Normal Distribution
Normal Distribution
Student t Distribution
Uniform Distribution
Binomial Distribution
Geometric Distribution
Negative Binomial Distribution
Poisson Distribution

Hypothesis Testing and Confidence Intervals

Concept	Notes	Implementation	Examples
Null Hypothesis
Hypothesis Testing
Type I and Type II Errors
Confidence Intervals
Multiple Comparisons
Analysis of Variance (ANOVA)
Analysis of Categorical Data
Resampling

Correlation and Regression

Concept	Notes	Implementation	Examples
Correlation
Covariance
Simple Linear Regression
Multiple Regression
Logistic Regression
Metrics

Time Series Analysis

Concept	Notes	Implementation	Examples
Time Series
Seasonality and Trends
Series
Difference Equations
Stationarity
Invertibility
Backward Shift Operator
Random Walk
Forecasting
Autoregressive Models
Moving Average Models
Autocorrelation Function
Autocovariance Function
Yule-Walker Equations

Spatial Statistics

Concept	Notes	Implementation	Examples
Point Processes
Spatial Autocorrelation
Geostatistics

How to Contribute

We encourage contributions that enhance the repository's value. To contribute:

1. Fork the repository.
2. Create your feature branch (git checkout -b feature/AmazingFeature).
3. Commit your changes (git commit -m 'Add some AmazingFeature').
4. Push to the branch (git push origin feature/AmazingFeature).
5. Open a Pull Request.

References

Online Courses and Educational Platforms

• Harvard University's Introduction to Probability
• edX: Fundamentals of Statistics

Books

• The Signal and the Noise: Why So Many Predictions Fail--but Some Don't
• The Black Swan: The Impact of the Highly Improbable Antifragile: Things That Gain from Disorder https://amzn.to/4mhWf7e
• Naked Statistics: Stripping the Dread from the Data
• How Not to Be Wrong: The Power of Mathematical Thinking
• Antifragile: Things That Gain from Disorder
• Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets
• SpringerLink: An Introduction to Statistical Learning
• SpringerLink: The Elements of Statistical Learning

Open Source eBooks

• Think Bayes by Allen Downey
• Online Statistics Education: An Interactive Multimedia Course
• OpenStax: Introductory Statistics 2e
• Introduction to Probability by Charles M. Grinstead and J. Laurie Snell (PDF)

Resources and Cheat Sheets

• Probability Cheatsheet on GitHub
• Allen Downey's Blog on Probability and Bayesian Stats
• Saylor Academy: Introductory Statistics
• Statistical Learning with Sparsity by Hastie, Tibshirani, and Wainwright
• Statistics How To: Probability and Statistics Main Index

Video Lectures and Playlists

• Oxford Playlist on Probability and Statistics

License

This project is licensed under the MIT License - see the LICENSE file for details.