with and denoting the shape parameters.
The mean and variance of the Geeta distribution are:
The Geeta distribution is sometimes parameterized in terms of its mean, , instead of . This results in the following probability mass function:
For this parameterization, the variance is
This probability mass function is also given in the form:
Dataplot supports both parameterizations (see the Note section below).
The cumulative distribution function is computed by summing the probability mass function.
where <x> is a positive integer variable, number, or parameter;
<shape> is a number, parameter, or variable that specifies the valuie of theta (or mu);
<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 Geeta cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = GETCDF(X,0.3,1.6)
PLOT GETCDF(X,0.3,1.6) FOR X = 1 1 20
To restore the THETA parameterization, enter the command
Consul (1990), "Geeta Distribution and its Properties", Communications in Statistics--Theory and Methods, 19, pp. 3051-3068.
set geeta definition theta 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 getcdf(x,0.3,1.8) for x = 1 1 20 . title Theta = 0.5, Beta = 1.5 plot getcdf(x,0.5,1.5) for x = 1 1 20 . title Theta = 0.7, Beta = 1.2 plot getcdf(x,0.7,1.2) for x = 1 1 20 . title Theta = 0.9, Beta = 1.1 plot getcdf(x,0.9,1.1) for x = 1 1 20 . end of multiplot . justification center move 50 97 text Cumulative Distributions for Geeta Distribution
Date created: 8/23/2006