Dataplot Vol 2 Vol 1

# TSSCDF

Name:
TSSCDF (LET)
Type:
Library Function
Purpose:
Compute the two-sided slope cumulative distribution function with shape parameters and .
Description:
The standard two-sided slope distribution has the following cumulative distribution function:

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> = TSSCDF(<x>,<alpha>,<theta>,<a>,<b>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a number, parameter, or variable containing values in the interval (a,b);
<y> is a variable or a parameter (depending on what <x> is) where the computed two-sided slope cdf 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 = TSSCDF(0.3,1.2,0.3)
LET Y = TSSCDF(X,1.5,2.2,0,5)
PLOT TSSCDF(X,1.5,2.2,0,5) FOR X = 0 0.01 5
Default:
None
Synonyms:
None
Related Commands:
 TSSPDF = Compute the two-sided slope probability density function. TSSPPF = Compute the two-sided slope percent 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 TSSCDF(X,ALPHA,THETA) FOR X = 0  0.01  1
END OF LOOP
END OF LOOP
.
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT Two-Sided Slope Cumulative Distribution Functions
```

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