
KUMCDFName:
with and denoting the shape parameters. 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:
scale = b  a The general form of the distribution can then be found by using the relation
This distribution has been proposed as a more tractable alternative to the beta distribution.
<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 Kumaraswamy cdf value is stored; <alpha> is a positive number, parameter, or variable 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 = KUMCDF(X,0.5,2) PLOT KUMCDF(X,2,3) FOR X = 0 0.01 1
CASE ASIS 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 KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . LET ALPHA = 1.5 LET BETA = 6 TITLE Alpha = ^alpha, Beta = ^beta PLOT KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . LET ALPHA = 1.5 LET BETA = 2 TITLE Alpha = ^alpha, Beta = ^beta PLOT KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . LET ALPHA = 1.5 LET BETA = 1 TITLE Alpha = ^alpha, Beta = ^beta PLOT KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . LET ALPHA = 0.5 LET BETA = 2 TITLE Alpha = ^alpha, Beta = ^beta PLOT KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . LET ALPHA = 0.5 LET BETA = 1 TITLE Alpha = ^alpha, Beta = ^beta PLOT KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . LET ALPHA = 0.5 LET BETA = 0.75 TITLE Alpha = ^alpha, Beta = ^beta PLOT KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . LET ALPHA = 0.5 LET BETA = 0.25 TITLE Alpha = ^alpha, Beta = ^beta PLOT KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . LET ALPHA = 1 LET BETA = 1 TITLE Alpha = ^alpha, Beta = ^beta PLOT KUMCDF(X,ALPHA,BETA) FOR X = 0 0.01 1 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Kumaraswamy Cumulative Distribution Functions
Date created: 11/27/2007 