Let's assume you are having a symmetric distribution and the following information: \begin{align} F^{-1}(x)=a \end{align} How to mathematically solve the following equation \begin{align} F^{-1}(1-x)=\:? \end{align}
2026-03-27 18:35:52.1774636552
inverse CDF and symmetrical distribution
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Considering that the first equation is
$$x=P(A\leq a)$$
Using symmetry you get
$$F^{-1}(1-x)=-a$$