Module 15:
Generating functions and distributional structure

Module 15

What this module is for

Both at a working level; stronger QR emphasis for characteristic functions and cumulants. The purpose is to provide an alternative to difficult convolution—not to reward symbolic manipulation for its own sake.

Lesson 15.1 · Core

Probability generating functions

Depth: Working proficiency

QT/QR relevance: Both; count distributions and compound models

Lesson 15.2 · Core

Moment generating functions and their limitations

Depth: Working proficiency

QT/QR relevance: Both, especially QR; distributional derivations

Lesson 15.3 · Research Depth

Characteristic functions and cumulants

Depth: Advanced / quant researcher depth — Extension

QT/QR relevance: QR; later limit theory and distributional models

Lesson 15.4 · Core

Compound distributions and method selection

Depth: Working proficiency

QT/QR relevance: Both; aggregated random activity

Assessment

Module 15 assessment

Open assessment · No submitted assessment yet