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.[1] The function is named after its graph's resemblance to a
boxcar, a type of
railroad car. 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] and is the
Heaviside step function. 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.