with p and r denoting the shape parameters. The r parameter is restricted to non-negative integers.
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 interval (0,1);
<p> is a number or parameter in the range (0.5,1) that specifies the first shape parameter;
<r> is a number or parameter denoting a positive integer that specifies the second shape parameter;
<y> is a variable or a parameter where the computed lost games ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = LOSPPF(P1,0.7,2)
PLOT LOSPPF(P,0.6,5) FOR P = 0 0.01 0.99
Kemp and Kemp (1968), "On a Distribution Associated with Certain Stochastic Processes", Journal of the Royal Statistical Society, Series B, 30, pp. 401-410.
Haight (1961), "A Distribution Analogous to the Borel-Tanner Distribution", Biometrika, 48, pp. 167-173.
Johnson, Kotz, and Kemp (1992), "Univariate Discrete Distributions", Second Edition, Wiley, pp. 445-447.
title size 3 tic label size 3 label size 3 legend size 3 height 3 multiplot scale factor 1.5 x1label displacement 12 y1label displacement 17 . 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 P = 0.6, R = 3 plot losppf(p,0.6,3) for p = 0 0.01 0.99 . title P = 0.7, R = 3 plot losppf(p,0.7,3) for p = 0 0.01 0.99 . title P = 0.8, R = 3 plot losppf(p,0.8,3) for p = 0 0.01 0.99 . title P = 0.9, R = 3 plot losppf(p,0.9,3) for p = 0 0.01 0.99 . end of multiplot . justification center move 50 97 text Percent Point for Lost Games
Date created: 6/20/2006