Dataplot Vol 2 Vol 1

# SEMCDF

Name:
SEMCDF (LET)
Type:
Library Function
Purpose:
Compute the semi-circular cumulative distribution function.
Description:
The semi-circular distribution is the distribution onto one axis of the points uniformly distributed within the unit circle. As such, it is useful for testing 2-dimensional uniformity.

The formula for the cumulative distribution function is:

with and r denoting the location and scale parameters, respectively.

The case where = 0 and r = 1 is referred to as the standard semi-circular distribution.

Syntax:
LET <y> = SEMCDF(<x>,<mu>,<r>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, number, or parameter;
<mu> is a variable, number, or parameter that specifies the location parameter;
<r> is a variable, number, or parameter that specifies the scale parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed semi-circular cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

If <mu> and <r> are omitted, they default to 0 and 1, respectively.

Examples:
LET A = SEMCDF(0.5)
LET A = SEMCDF(0.5,0,5)
LET X2 = SEMCDF(X1)
Default:
None
Synonyms:
None
Related Commands:
 SEMPDF = Compute the semi-circular probability density function. SEMPPF = Compute the semi-circular percent point function. UNIPDF = Compute the uniform probability density function. UNICDF = Compute the uniform cumulative distribution function. UNIPPF = Compute the uniform percent point function. NORCDF = Compute the normal cumulative distributoin function. NORPDF = Compute the normal probability density function. NORPPF = Compute the normal percent point function.
Reference:
Johnson and Kotz (1970), Continuous Univariate Distributions - 2, Houghton Mifflin, (chapter 25).

Filliben (1969), Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution, unpublished Ph.d dissertation, Princeton University, (pp. 21-44, 229-231).

Applications:
Distributional Modeling
Implementation Date:
1994/4: Implemented for the standard case
2006/10: Implemented for the general case
Program:
```
YLIMITS 0 1
MAJOR YTIC NUMBER 6
MINOR YTIC NUMBER 1
YTIC DECIMAL 1
XLIMITS -1 1
XTIC OFFSET 0.1 0.1
TITLE AUTOMATIC
PLOT SEMCDF(X) FOR X = -1 0.01 1
```

Date created: 1/8/2008
Last updated: 1/8/2008