with p denoting the shape parameter and denoting the gamma function (HELP GAMMA for details).
Dataplot computes the Yule probability density function using the log gamma function. The Yule distribution has increasingly long tails as p goes to zero. Currently, Dataplot limits the Yule ppf function to the case where p >= 0.1.
The cumulative distribution function is the sum from 0 to x. The percent point function is the inverse of the cumulative distribution function. That is, given the probability, the appropriate value of x is returned. The percent point is determined by computing the terms of the Yule cdf function until the requested probability value is obtained.
where <x> is a non-negative integer number, parameter, or variable in the interval (0,1);
<p> is a positive number, parameter, or variable that specifies the shape parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed Yule ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = YULPPF(X,P)
PLOT YULPPF(X,2) FOR X = 0 0.01 0.95
X1LABEL Probability Y1LABEL X LABEL CASE ASIS X1LABEL DISPLACEMENT 12 Y1LABEL DISPLACEMENT 12 MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 100 XTIC OFFSET 0.1 0.1 LINE BLANK SPIKE ON TITLE AUTOMATIC X1LABEL X Y1LABEL PROBABILITY TITLE SIZE 3 PLOT YULPPF(P,0.5) FOR P = 0 0.01 0.95 PLOT YULPPF(P,1) FOR P = 0 0.01 0.99 PLOT YULPPF(P,1.5) FOR P = 0 0.01 0.99 PLOT YULPPF(P,2) FOR P = 0 0.01 0.99 END OF MULTIPLOT
Date created: 7/7/2004