Dataplot Vol 2 Vol 1

# GTRPPF

Name:
GTRPPF (LET)
Type:
Library Function
Purpose:
Compute the generalized trapezoidal percent point function.
Description:
The generalized trapezoidal distribution has the following cumulative distribution function:

The algorithm for the generalized trapezoid percent point function is to compute the cumulative distribution function at the points a, b, c, and d to determine an appropriate bracketing interval. Then the appropriate equation above is inverted to find the value of the percent point function. For the interval b <= x < c, a bisection method is used.

Syntax:
LET <y> = GTRPPF(<p>,<a>,<b>,<c> <d>,<nu1>,<nu3>,<alpha>)
<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;
<nu1> is a number, parameter, or variable that specifies the fifth shape parameter;
<nu3> is a number, parameter, or variable that specifies the sixth shape parameter;
<alpha> is a number, parameter, or variable that specifies the seventh shape parameter;
<y> is a variable or a parameter (depending on what <p> is) where the computed ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = GTRPPF(0.95,0,0.2,0.8,1,2,2,0.5)
LET Y = GTRPPF(P,0,0.2,0.8,1,2,2,0.5)
LET Y = GTRPPF(P,A,B,C,D,NU1,NU3,ALPHA)
Default:
None
Synonyms:
None
Related Commands:
 GTRCDF = Compute the generalized trapezoidal cumulative distribution function. GTRPDF = Compute the generalized trapezoidal probability density function. TRAPDF = Compute the trapezoidal probability density 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.
Reference:
"Generalized Trapezoidal Distributions", van Dorp and Kotz, Metrika, Vol. 58, Issue 1, July, 2003.
Applications:
Distributional Modeling
Implementation Date:
2004/1
Program:
```
TITLE GENERALIZED TRAPEZOIDAL DISTRIBUTION
LABEL CASE ASIS
X1LABEL Probability
Y1LABEL X
LET A = 0
LET B = 0.2
LET C = 0.8
LET D = 1
LET NU1 = 1.5
LET NU3 = 2.2
LET ALPHA = 0.5
PLOT GTRPPF(P,A,B,C,D,NU1,NU3,ALPHA) FOR P = 0  0.01  1
```

Date created: 2/3/2004
Last updated: 2/3/2004