Trapezoidal distributions may be appropriate for modeling processes that can be represented by the following three stages:

1. a growth stage
2. a period of relative stability stage
3. a decay stage

The trapezoidal model is probably the simplest model of this type (i.e., the growth and decline stages are linear and the stability stage is constant). The generalized trapezoidal distribution allows more flexibility in modeling these stages.

The uniform (no growth or decay stages) and triangular (no stable stage) distributions are special cases of the trapezoidal distribution.

f(x,a,b,c,d) =   

u(x-a)/(b-a), for a⇐x less than b   

u, for b⇐x less than c   

u(d-x)/(d-c), for c⇐x less than d   

0 otherwise

where u=2/(d+c-b-a).

support a ⇐ x ⇐ d