The probability mass function of the Borel-Tanner distribution is
with and k denoting the shape parameters. The k shape parameter is a positive integer and = l.
The cumulative distribution function is computed by summing the probability mass function. The percent point function is the inverse of the cumulative distribution function and is obtained by computing the cumulative distribution function until the specified probability is reached.
where <p> is a variable, number, or parameter in the range (0,1);
<lambda> is a number or parameter in the range (0,1) that specifies the first shape parameter;
<k> is a number or parameter denoting a positive integer that specifies the first shape parameter;
<y> is a variable or a parameter where the computed Borel-Tanner ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = BTAPPF(P1,0.3,2)
PLOT BTAPPF(P,0.4,2) FOR P = 0 0.01 0.99
Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 394-396.
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 . xlimits 0 1 major xtic mark number 6 minor xtic mark number 3 line blank spike on . multiplot 2 2 . title Lambda = 0.3 plot btappf(p,0.3,1) for p = 0 0.01 0.99 . title Lambda = 0.5 plot btappf(p,0.5,1) for p = 0 0.01 0.99 . title Lambda = 0.7 plot btappf(p,0.7,1) for p = 0 0.01 0.99 . title Lambda = 0.9 plot btappf(p,0.9,1) for p = 0 0.01 0.99 . end of multiplot . justification center move 50 97 text Percent Point Functions for Borel-Tanner
Date created: 6/5/2006