Use of $\arg$ function

Question

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?

score 1 · Accepted Answer · answered May 09 '16 at 09:38

1

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 $\Phi$.

answered May 09 '16 at 09:38

Ulrik

2,557

That's it! Thank you for pointing it out. So easy. Didn't think of the inverse image. – Xiphias May 09 '16 at 17:23

Use of $\arg$ function

1 Answers1