
GTLCDFName:
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:
scale = b  a
<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.
LET Y = GTLCDF(X,0.5,2) PLOT GTLCDF(X,2,3) FOR X = 0 0.01 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 