 Dataplot Vol 2 Vol 1

# TSSPPF

Name:
TSSPPF (LET)
Type:
Library Function
Purpose:
Compute the two-sided slope percent point function with shape parameters and .
Description:
The percent point function for the standard two-sided slope distribution can be found by solving the following quadratic equation: where The above equations have two possible roots. The root that lies in the (0,1) interval is the one that is kept.

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> = TSSPPF(<p>,<alpha>,<theta>,<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 two-sided slope ppf value is stored;
<alpha> is a number, parameter, or variable in the interval (0,2) that specifies the first shape parameter;
<theta> is a number, parameter, or variable in the interval (a,b) that specifies the second shape parameter;
<a> is a number, parameter, or variable that specifies the lower bound;
<b> is a number, parameter, or variable that specifies the upper bound;
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 = TSSPPF(0.95,1.2,0.3)
LET Y = TSSPPF(P,1.5,2.2,0,5)
PLOT TSSPPF(X,1.5,2.2,0,5) FOR P = 0 0.01 1
Default:
None
Synonyms:
None
Related Commands:
 TSSCDF = Compute the two-sided slope cumulative distribution function. TSSPDF = Compute the two-sided probability density point function. SLOPDF = Compute the slope probability density function. OGIPDF = Compute the ogive probability density function. TSOPDF = Compute the two-sided ogive probability density function. TOPPDF = Compute the Topp and Leone probability density function. RGTPDF = Compute the generalized reflected Topp and Leone probability density function. GTLPDF = Compute the generalized Topp and Leone probability density function. TSPPDF = Compute the two-sided power probability density function. BETPDF = Compute the beta 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:
```
MULTIPLOT 3 3
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 3
TITLE OFFSET 2
TITLE CASE ASIS
LABEL CASE ASIS
CASE ASIS
.
LET THETAV = DATA 0.25  0.50 0.75
LET ALPHAV = DATA 0.5  1.0  1.5
.
LOOP FOR K = 1 1 3
LET THETA = THETAV(K)
LOOP FOR L = 1 1 3
LET ALPHA = ALPHAV(L)
TITLE Theta = ^THETA, Alpha = ^ALPHA
PLOT TSSPPF(P,ALPHA,THETA) FOR P = 0  0.01  1
END OF LOOP
END OF LOOP
.
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT Two-Sided Slope Percent Point Functions
``` Date created: 11/07/2007
Last updated: 11/07/2007