Logarithmically concave function

A function ${\displaystyle f}$ is logarithmically concave (or log-concave for short), if its natural logarithm ${\displaystyle \ln(f(x))}$, is concave. Every concave function is log-concave, however the reverse does not necessarily hold (e.g., ${\displaystyle \exp\{-x^{2}\}}$).

In parallel, a function is log-convex if its natural log is convex.

See also

• Convex function