![]() |
CONPPFName:
![]()
with The mean and variance of the Consul distribution are:
![]()
The Consul distribution is also parameterized in terms of
its mean,
![]()
![]() For this parameterization, the mean and variance are:
![]()
Dataplot supports both parameterizations (see the Note section below). Dataplot computes the cumulative distribution function using the following recurrence relation given on page 320 of Consul and Famoye:
![]()
where The Consul percent point function is computed by summing the cumulative distribution function until the specified probability is obtained.
<SUBSET/EXCEPT/FOR qualification> where <p> is a positive integer variable, number, or parameter in the range (0,1); <shape> is a number, parameter, or variable that specifies the valuie of theta (or mu); <m> 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 Consul ppf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = CONPPF(P,0.3,1.6) PLOT CONPPF(P,0.3,1.6) FOR P = 0 0.01 0.99
To restore the THETA parameterization, enter the command
Famoye (1997), "Generalized Geometric and Some of its Applications", Journal of Mathematical Sciences, 8, pp. 1-13. Consul (1990), "New Class of Location-Parameter Discrete Probability Distributions and Their Chaacterizations", Communications in Statistics--Theory and Methods, 19, pp. 4653-4666.
set consul 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, M = 1.8 plot conppf(p,0.3,1.8) for p = 0 0.01 0.99 . title Theta = 0.5, M = 1.5 plot conppf(p,0.5,1.5) for p = 0 0.01 0.99 . title Theta = 0.7, M = 1.2 plot conppf(p,0.7,1.2) for p = 0 0.01 0.99 . title Theta = 0.9, M = 1.1 plot conppf(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 Consul Distribution ![]()
Date created: 8/23/2006 |