Question. What is a notation for the histogram's bar corresponding to the "leftmost local maxima"?
Maybe what proposed in Peak / local maxima notation can be adapted to denote the bar corresponding to the "leftmost local maxima" in a histogram, but I am not sure about it.
My attempt. I was thinking about the following, but I am not sure:
if $f(x)$ is the frequency of occurrence of a quantity $x$ in a histogram, then we might identify the position of the "leftmost local maxima",
$$ {\displaystyle {\underset {x}{\operatorname {min\,(arg\,local\,max} }}\,f(x)) := {\operatorname {min\, \{ x \mid \exists r>0 \, s.t. \forall x' \in (x-r,x+r), f(x') \leq f(x) \}}}} $$
Therefore the histogram's bar corresponding to the "leftmost local maxima" might be written as:
$$ f({\displaystyle {\underset {x}{\operatorname {min\,(arg\,local\,max} }}\,f(x))}) $$
Does this notation make sense?