Dataplot Vol 2 Vol 1

# RPOCDF

Name:
RPOCDF (LET)
Type:
Library Function
Purpose:
Compute the reflected power cumulative distribution function with shape parameter c.
Description:
The standard reflected power distribution has the following cumulative distribution function:

with c 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

The reflected power distribution is a special case of the beta distribution where the first shape parameter = 1 (the power distribution is a special case of the beta distribution where the second shape parameter = 1).

Syntax:
LET <y> = RPOCDF(<x>,<c>,<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 reflected power cdf value is stored;
<c> 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 = RPOCDF(0.3,0.2)
LET Y = RPOCDF(X,0.5,0,5)
PLOT RPOCDF(X,2.3) FOR X = 0 0.01 1
Default:
None
Synonyms:
None
Related Commands:
 RPOPDF = Compute the reflected power probability density function. RPOPPF = Compute the reflected power percent point function. RPOHAZ = Compute the reflected power hazard function. RPOCHAZ = Compute the reflected power cumulative hazard function. POWPDF = Compute the power probability density function. BETPDF = Compute the beta 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. TRIPDF = Compute the triangular probability density function. TRAPDF = Compute the trapezoid probability density function. UNIPDF = Compute the uniform 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, pp. 199-201.
Applications:
Distributional Modeling
Implementation Date:
2007/12
Program:
```
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR
.
LET C  = 0.5
TITLE C = ^c
PLOT RPOCDF(X,C) FOR X = 0  0.01  1
.
LET C  = 1
TITLE C = ^c
PLOT RPOCDF(X,C) FOR X = 0  0.01  1
.
LET C  = 1.5
TITLE C = ^c
PLOT RPOCDF(X,C) FOR X = 0  0.01  1
.
LET C  = 2
TITLE C = ^c
PLOT RPOCDF(X,C) FOR X = 0  0.01  1
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Reflected Power Cumulative Distribution Functions
```

Date created: 12/17/2007
Last updated: 12/17/2007