
GLSCDFName:
with and denoting the shape parameters and denoting the gamma function (enter HELP GAMMA for details). The cumulative distribution function is computed using the following recurrence relation given on pages 228229 of Consul and Famoye:
with
<SUBSET/EXCEPT/FOR qualification> where <x> is a positive integer variable, number, or parameter; <theta> is a number, parameter, or variable in the range (0,1) that specifies the first shape parameter; <beta> is a number, parameter, or variable that specifies the second shape parameter; <y> is a variable or a parameter (depending on what <x> is) where the computed generalized logarithmic series cdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = GLSCDF(X,0.3,1.6) PLOT GLSCDF(X,0.3,1.6) FOR X = 1 1 20
title size 3 tic label size 3 label size 3 legend size 3 height 3 x1label displacement 12 y1label displacement 15 . multiplot corner coordinates 0 0 100 95 multiplot scale factor 2 label case asis title case asis case asis tic offset units screen tic offset 3 3 title displacement 2 y1label Probability x1label X . ylimits 0 1 major ytic mark number 6 minor ytic mark number 3 xlimits 0 20 line blank spike on . multiplot 2 2 . title Theta = 0.3, Beta = 1.8 plot glscdf(x,0.3,1.8) for x = 1 1 20 . title Theta = 0.5, Beta = 1.5 plot glscdf(x,0.5,1.5) for x = 1 1 20 . title Theta = 0.7, Beta = 1.2 plot glscdf(x,0.7,1.2) for x = 1 1 20 . title Theta = 0.9, Beta = 1.1 plot glscdf(x,0.9,1.1) for x = 1 1 20 . end of multiplot . justification center move 50 97 text Cumulative Distribution for Generalized Logarithmic Series
Date created: 8/23/2006 