Dataplot Vol 2 Vol 1

# SLOPPF

Name:
SLOPPF (LET)
Type:
Library Function
Purpose:
Compute the slope percent point function with shape parameter .
Description:
The standard slope distribution has the following percent point function:

with denoting the shape parameter.

This distribution can be extended with lower and upper bound parameters. If a and b denote the lower and upper bounds, respectively, then the location and scale parameters are:

location = a
scale = b - a

The general form of the distribution can then be found by using the relation

Syntax:
LET <y> = SLOPPF(<p>,<alpha>,<a>,<b>)
<SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or variable containing values in the interval (0,1);
<y> is a variable or a parameter (depending on what <p> is) where the computed slope ppf value is stored;
<alpha> is a positive number, parameter, or variable that specifies the shape parameter;
<a> is a number, parameter, or variable that specifies the lower limit;
<b> is a number, parameter, or variable that specifies the upper limit;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

If <a> and <b> are omitted, they default to 0 and 1, respectively.

Examples:
LET A = SLOPPF(0.95,0.2)
LET Y = SLOPPF(X,0.5,0,5)
PLOT SLOPPF(P,2,0,3) FOR P = 0 0.01 1
Default:
None
Synonyms:
None
Related Commands:
 SLOCDF = Compute the slope cumulative distribution function. SLOPDF = Compute the slope probability density function. TSSPDF = Compute the two-sided slope probability density function. OGIPDF = Compute the ogive probability density function. TOPPDF = Compute the Topp and Leone probability density function. RGTPDF = Compute the generalized reflected slope probability density function. GTLPDF = Compute the generalized slope probability density function. TSPPDF = Compute the two-sided power probability density function. BETPDF = Compute the alpha probability density function. TRIPDF = Compute the triangular probability density function. TRAPDF = Compute the trapezoid probability density function. UNIPDF = Compute the uniform probability density function. POWPDF = Compute the power probability density function. JSBPDF = Compute the Johnson SB probability density function.
Reference:
Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications", World Scientific, chapter 8.
Applications:
Distributional Modeling
Implementation Date:
2007/10
Program:
```
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET ALPHA  = 0.5
TITLE Alpha = ^alpha
PLOT SLOPPF(P,ALPHA) FOR P = 0  0.01  1
.
LET ALPHA  = 1
TITLE Alpha = ^alpha
PLOT SLOPPF(P,ALPHA) FOR P = 0  0.01  1
.
LET ALPHA  = 1.5
TITLE Alpha = ^alpha
PLOT SLOPPF(P,ALPHA) FOR P = 0  0.01  1
.
LET ALPHA  = 2
TITLE Alpha = ^alpha
PLOT SLOPPF(P,ALPHA) FOR P = 0  0.01  1
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Slope Percent Point Functions
```

Date created: 11/07/2007
Last updated: 11/07/2007