a ≤ b ≤ c ≤ d
Trapezoidal distributions may be appropriate for modeling processes that can be represented by the following three stages:
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. Syntax:
where <x> is a variable, number, or parameter containing values in the interval (a,d);
<a> is a number, parameter, or variable that specifies the first shape parameter;
<b> is a number, parameter, or variable that specifies the second shape parameter;
<c> is a number, parameter, or variable that specifies the third shape parameter;
<d> is a number, parameter, or variable that specifies the fourth shape parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed pdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = TRAPDF(0.5,A,B,C,D)
TITLE TRAPEZOIDAL DISTRIBUTION LET A = 0 LET B = 1 LET C = 5 LET D = 10 PLOT TRAPDF(X,A,B,C,D) FOR X = A 0.1 10
Date created: 2/3/2004