
GTLPPFName:
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:
scale = b  a
<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 generalized Topp and Leone pdf 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 = GTLPPF(P,0.5,2) PLOT GTLPPF(P,2,3) FOR P = 0 0.01 1
2007/9: Replaced bisection computation with explicit formula 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 GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . LET ALPHA = 1.5 LET BETA = 6 TITLE Alpha = ^alpha, Beta = ^beta PLOT GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . LET ALPHA = 1.5 LET BETA = 2 TITLE Alpha = ^alpha, Beta = ^beta PLOT GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . LET ALPHA = 1.5 LET BETA = 1 TITLE Alpha = ^alpha, Beta = ^beta PLOT GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . LET ALPHA = 0.5 LET BETA = 2 TITLE Alpha = ^alpha, Beta = ^beta PLOT GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . LET ALPHA = 0.5 LET BETA = 1 TITLE Alpha = ^alpha, Beta = ^beta PLOT GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . LET ALPHA = 0.5 LET BETA = 0.75 TITLE Alpha = ^alpha, Beta = ^beta PLOT GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . LET ALPHA = 0.5 LET BETA = 0.25 TITLE Alpha = ^alpha, Beta = ^beta PLOT GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . LET ALPHA = 1 LET BETA = 1 TITLE Alpha = ^alpha, Beta = ^beta PLOT GTLPPF(P,ALPHA,BETA) FOR P = 0 0.01 1 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Generalized Topp and Leone PPF Functions
Date created: 9/24/2007 