TITLE: Logarithm of Gaussian function is whether convex or nonconvex?
QUESTION [7 upvotes]: I have a gaussian distribution such as
$$P(x)=\frac {1}{\sqrt {2\pi}\sigma}e^{-\frac {(x-\mu)^2}{2\sigma^2}} $$
As my knowledge, $P(x)$ is non convex function interm of $x$. However, if I map it to $log$ space, Does it become convex function? If it is convex, please prove help me. Thanks in advance

REPLY [3 votes]: The Gaussian density function is quasiconcave but not concave. Moreover, it is log-concave because log P(x) is essentially a negative quadratic function.