Dataplot Vol 2 Vol 1

# TSOCDF

Name:
TSOCDF (LET)
Type:
Library Function
Purpose:
Compute the two-sided ogive cumulative distribution function with shape parameters n and
Description:
The two-sided ogive cumulative distribution function can be computed using the following relation to the ogive cumulative distribution function:

with F and G denoting the cumulative distribution functions of the two-sided ogive and the ogive distributions, respectively. This relation is given on page 230 of Kotz and Van Dorp (see Reference section below).

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

Kotz and Van Dorp note that the two-sided ogive distribution is smooth at the reflection point (x = ). This is in contrast to the two-sided slope and two-sided power distributions, which are not smooth at the relection point.

Syntax:
LET <y> = TSOCDF(<x>,<n>,<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 ogive cdf value is stored;
<n> is a number, parameter, or variable in the interval (≥ 0.5) 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 = TSOCDF(0.3,1.2,0.3)
LET Y = TSOCDF(X,1.5,2.2,0,5)
PLOT TSOCDF(X,1.5,2.2,0,5) FOR X = 0 0.01 5
Default:
None
Synonyms:
None
Related Commands:
 TSOPDF = Compute the two-sided ogive probability density function. TSOPPF = Compute the two-sided ogive percent point function. OGIPDF = Compute the ogive probability density function. TSSPDF = Compute the two-sided slope probability density function. TSPPDF = Compute the two-sided power probability density function. POWPDF = Compute the power probability density function. SLOPDF = Compute the slope probability density function. BETPDF = Compute the Beta 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 NV = DATA 0.5  1.5  2.5
.
LOOP FOR K = 1 1 3
LET THETA = THETAV(K)
LOOP FOR L = 1 1 3
LET N = NV(L)
TITLE Theta = ^THETA, N = ^N
PLOT TSOCDF(X,N,THETA) FOR X = 0  0.01  0.99
END OF LOOP
END OF LOOP
.
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT Two-Sided Ogive Cumulative Distribution Functions
```

Date created: 12/13/2007
Last updated: 12/13/2007