Suppose we have a function $g(x)$ which is concave in $x$. Is it still the case that $g(1-F(x))$ is concave with $F(x)$ a cdf? I have problems with (dis)proving it. Thanks a lot!
2026-04-07 06:17:16.1775542636
Concavity function
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If you check the rules for concavity of compositions, you will find statements involving monotonicity of $g$ and convexity of $F$. The statement is currently clearly false for $g(x)=x$ and any cdf.