Introduction

Content Covered

This textbook is designed to offer a comprehensive introduction to probability distributions, with a focus on both theoretical foundations and practical applications. The material is structured to guide the reader through key concepts, starting from elementary distributions and moving to more advanced topics. Along the way, you will encounter topics such as:

• Discrete and Continuous Distributions Covering foundational distributions like the Binomial, Poisson, Normal, and Exponential, and progressing to more specialized ones such as the Beta, Gamma, and Laplace.
• Parameter Estimation Techniques Exploring the method of moments, Maximum Likelihood Estimation (MLE), and Bayesian approaches to inferring distribution parameters.
• Goodness-of-Fit and Diagnostic Tools Providing methods for assessing how well a distribution fits observed data, including the Cramér-von Mises and Kolmogorov-Smirnov statistics.
• Mixture and Compound Distributions Introducing methods for combining distributions to model complex phenomena.
• Multivariate Distributions and Dependencies Discussing joint distributions, copulas, and measures of dependence, including correlation and mutual information.

Differences with this Book

What sets this textbook apart is its emphasis on interactive examples. Through the integration of dynamic tools and visualizations, readers are encouraged to engage with the material directly—manipulating distributions, exploring their properties, and testing hypotheses in real-time. This hands-on approach enhances comprehension and deepens intuition, turning abstract concepts into tangible experiences.