Dataplot Vol 2 Vol 1

# RGTPPF

Name:
RGTPPF (LET)
Type:
Library Function
Purpose:
Compute the reflected generalized Topp and Leone percent point function with shape parameters alpha and beta.
Description:
The standard reflected generalized Topp and Leone distribution has the following percent point function:

with and denoting the shape parameters.

The standard distribution can be generalized with lower and upper bound parameters, a and b, respectively, by utilizing the following relation:

The lower and upper limits are related to the location and scale parameters as follows:

location = a
scale = b - a
Syntax:
LET <y> = RGTPDF(<p>,<alpha>,<beta>,<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 reflected generalized Topp and Leone ppf value is stored;
<alpha> is a number, parameter, or variable in the interval (0, 2) that specifies the first shape parameter;
<beta> is a positive number, parameter, or variable that specifies the second 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 = RGTPPF(0.95,0.2,1.2)
LET Y = RGTPPF(P,0.5,2)
PLOT RGTPPF(P,2,3) FOR P = 0 0.01 1
Default:
None
Synonyms:
None
Related Commands:
 RGTCDF = Compute the reflected generalized Topp and Leone cumulative distribution function. RGTPDF = Compute the reflected generalized Topp and Leone probability density function. GTLPDF = Compute the generalized Topp and Leone probability density function. TOPPDF = Compute the 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 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 7.
Applications:
Distributional Modeling
Implementation Date:
2007/2
Program:
```
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 3 3
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 3
.
LET ALPHA = 2
LET BETA  = 3
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 6
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 2
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 2
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 0.75
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 0.25
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
LET ALPHA = 1
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTPPF(P,ALPHA,BETA) FOR P = 0  0.01  1
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Reflected Generalized Topp and Leone PPF Functions
```

Date created: 9/18/2007
Last updated: 9/18/2007
Please email comments on this WWW page to alan.heckert@nist.gov.