Boxcar function

In mathematics, a boxcar function is any function which is zero over the entire real line except for a single interval where it is equal to a constant (A). It can be expressed in terms of the uniform distribution as:

${\textrm {boxcar}}(x)=(b-a)A\,f(a,b;x)$

where f(a,b;x)  is the uniform distribution of x for the interval from a to b. As with most such discontinuous functions, there is a question of the value at the transition points. These values are probably best chosen for each individual application.