with and n denoting the shape parameters.
Some sources parameterize this distribution with s = - 1 (so that the distribution is defined for s > 0).
The cumulative distribution 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 until the specified probability is obtained.
where <p> is a variable, number, or parameter in the range (0,1);
<alpha> is a number or parameter greater than 1 that specifies the first shape parameter;
<n> is a number or parameter that is a positive integer that specifies the second shape parameter;
<y> is a variable or a parameter where the computed Zipf ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = ZIPPPF(X1,2.3,1000)
PLOT ZIPPPF(X,2.3,100) FOR X = 1 1 100
multiplot corner coordinates 0 0 100 95 multiplot scale factor 2 case asis label case asis title case asis tic offset units screen tic offset 3 3 title displacement 2 y1label displacement 17 x1label displacement 12 . x1label Probability xlimits 0 1 major xtic mark number 6 minor xtic mark number 3 y1label X line blank spike on . multiplot 2 2 let n = 100 . let alpha = 1.5 title Alpha = ^alpha plot zipppf(p,alpha,n) for p = 0 0.01 1 . let alpha = 2.0 title Alpha = ^alpha plot zipppf(p,alpha,n) for p = 0 0.01 1 . let alpha = 2.5 title Alpha = ^alpha plot zipppf(p,alpha,n) for p = 0 0.01 1 . let alpha = 3.0 title Alpha = ^alpha plot zipppf(p,alpha,n) for p = 0 0.01 1 . end of multiplot . justification center move 50 97 text Zipf Percent Point Functions
Date created: 6/5/2006