Let $X$ be a random variable, and for a given $c>0$ let $f_c:\mathbb R\to [0,\infty)$ be a measurable function defined by $x\mapsto \max\{x-c,0\}$. Write $Y:=f_c$.
I have not been able to find a name in the literature for this function. Note that $$ Y=\begin{cases} X-c,&c<X,\\ 0,&c\geqslant X, \end{cases} $$ or more succinctly $$ Y = (X-c)\cdot\mathsf 1_{(c,\infty)}(X). $$
Having a definite name for this function would be very helpful.
I think we call them as "HINGE FUNCTIONS".
Multivariate adaptive regression splines, implemented by the Earth class, is a flexible regression method that automatically searches for interactions and non-linear relationships. Earth models can be thought of as linear models in a higher dimensional basis space. Each term in an Earth model is a product of so called “hinge functions”. A hinge function is a function that’s equal to its argument where that argument is greater than zero and is zero everywhere else.
h(x−t) = [x−t]+ = { x−t,x>t; 0,x≤t;