Dataplot Vol 2 Vol 1

# GTLCDF

Name:
GTLCDF (LET)
Type:
Library Function
Purpose:
Compute the generalized Topp and Leone cumulative distribution function with shape parameters and .
Description:
The generalized Topp and Leone distribution has the following cumulative distribution function:

with and denoting the shape parameters and a and b the lower and upper limits, respectively.

The case where a = 0 and b = 1 is referred to as the standard generalized Topp and Leone distribution. It has the following cumulative distribution function:

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

location = a
scale = b - a
Syntax:
LET <y> = GTLCDF(<x>,<alpha>,<beta>,<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 generalized Topp and Leone cdf 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 = GTLCDF(0.3,0.2,1.2)
LET Y = GTLCDF(X,0.5,2)
PLOT GTLCDF(X,2,3) FOR X = 0 0.01 1
Default:
None
Synonyms:
None
Related Commands:
 GTLPDF = Compute the generalized Topp and Leone probability density function. GTLPPF = Compute the generalized Topp and Leone percent point function. RGTPDF = Compute the reflected 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 1:

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 GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 6
TITLE Alpha = ^alpha, Beta = ^beta
PLOT GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 2
TITLE Alpha = ^alpha, Beta = ^beta
PLOT GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 2
TITLE Alpha = ^alpha, Beta = ^beta
PLOT GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 0.75
TITLE Alpha = ^alpha, Beta = ^beta
PLOT GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 0.25
TITLE Alpha = ^alpha, Beta = ^beta
PLOT GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 1
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT GTLCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
END OF MULTIPLOT

Date created: 9/24/2007
Last updated: 9/24/2007