Description

Stable distributions play a central role in probability theory, statistics, and applications where heavy tails and skewness are present. This course offers a structured journey from foundational concepts to advanced techniques in the study of stable laws. Beginning with the theoretical motivation and historical development, we will cover key definitions, the meaning of stability, and the significance of the Generalized Central Limit Theorem.

Students will gain a deep understanding of the four parameters governing stable distributions and their impact on shape and behavior. The course emphasizes the role of the characteristic function as the defining tool for stable distributions and demonstrates how probability density functions can be computed via inverse Fourier transforms. Parameter estimation methods will be introduced, along with hands-on practice applying these techniques to real-world data.

By the end of the course, participants will be able to:

• Recognize contexts where stable distributions are applicable,

• Understand their mathematical structure,

• Compute and estimate their parameters,

• Apply stable distribution models to practical problems in fields such as finance, physics, and signal processing.

This course is designed for students and professionals with a background in probability, statistics, or applied mathematics who are interested in extending their knowledge to the study of non-Gaussian phenomena.