I know that $\underset{x}{\operatorname{argmax}}f(x)$ is defined as the value at which $f(x)$ has its maximum. There is also $\underset{x}{\operatorname{argmin}}$.

However, in statistics, I often write something like $\Phi(z)=0.95$, and I am then looking for the value z that satisfies the equation.

Thus, this seems like something as $\underset{z, \textrm{where} f(z)=0.95}{\operatorname{argspecificvalue}}f(z)$.

Does something like that exist, i.e. how can I define the value z that satisfies the equation and how would one write it?


closed as unclear what you're asking by John B, Ferra, Wojowu, Frits Veerman, Daniel W. Farlow May 9 '16 at 12:08

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There could be more such values. What you are looking for is to determine the set $$\Phi^{-1}(0.95) = \{ z : \Phi(z) = 0.95 \}$$ It is called the inverse image of $0.95$ under $\Phi$.

  • $\begingroup$ That's it! Thank you for pointing it out. So easy. Didn't think of the inverse image. $\endgroup$ – Xiphias May 9 '16 at 17:23

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