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. The percent point function is computed by summing the cumulative distribution function until the appropriate probability is reached.
where <p> is a positive integer variable, number, or parameter in the interval (0,1);
<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 <p> is) where the computed Geeta ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = GETPPF(P,0.3,1.6)
PLOT GETPPF(P,0.3,1.6) FOR P = 0 0.01 0.99
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 x1label Probability y1label X . xlimits 0 1 major xtic mark number 6 minor xtic mark number 3 . multiplot 2 2 . title Theta = 0.3, Beta = 1.8 plot getppf(p,0.3,1.8) for p = 0 0.01 0.99 . title Theta = 0.5, Beta = 1.5 plot getppf(p,0.5,1.5) for p = 0 0.01 0.99 . title Theta = 0.7, Beta = 1.2 plot getppf(p,0.7,1.2) for p = 0 0.01 0.99 . title Theta = 0.9, Beta = 1.1 plot getppf(p,0.9,1.1) for p = 0 0.01 0.99 . end of multiplot . justification center move 50 97 text Percent Point Functions for Geeta Distribution
Date created: 8/23/2006