---
tag: 0N2SP6K9ZC
kind: concept
name: Cumulant generating function
aliases: [cumulant-generating-function, cgf]
msc: ["60E10"]
sources:
  - url: https://en.wikipedia.org/wiki/Cumulant
    locator: Definition
---

## Summary

The cumulant generating function of a real random variable is the logarithm of its moment-generating function. Its Taylor coefficients at $0$ are the cumulants.
The node [[cumulant generating function|0Q2QC81VTW]] gives the precise definition.