TRAPDF

TRAPDF (LET)

Library Function

Compute the trapezoidal probability density function.

The trapezoidal distribution has the following probability density function:

where

u = 2/(d + c - b - a)
a ≤ b ≤ c ≤ d

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.

LET <y> = TRAPDF(<x>,<a>,<b>,< c><d>)
                        <SUBSET/EXCEPT/FOR qualification>
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(0.5,0,0.25,0.75,1)
LET A = TRAPDF(0.5,A,B,C,D)

None

None

TRACDF	= Compute the trapezoidal cumulative distribution function.
TRAPPF	= Compute the trapezoidal percent point function.
TRIPDF	= Compute the triangular probability density function.
UNIPDF	= Compute the uniform probability density function.
SEMPDF	= Compute the semi-circular probability density function.
NORPDF	= Compute the normal probability density function.

"Generalized Trapezoidal Distributions", van Dorp and Kotz, Metrika, Vol. 58, Issue 1, July, 2003.

Distributional Modeling

2004/1

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