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, which we will denote by A. The boxcar function can be expressed in terms of the uniform distribution as

where f(a,b;x)  is the uniform distribution of x for the interval [a, 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.