
ZETPPFName:
with denoting the shape parameter and denoting the Riemann zeta function
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 inversre of the cumulative distribution function and is obtained by computing the cumulative distribution function until the desired probability is reached. The zeta distribution can have very long tails as the value of alpha gets close to 1. Dataplot will return an error message if the percent point value exceeds the maximum machine integer value.
<SUBSET/EXCEPT/FOR qualification> where <p> is a variable, number, or parameter in the interval (0,1); <alpha> is a number or parameter greater than 1 that specifies the shape parameter; <y> is a variable or a parameter where the computed zeta ppf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET Y = ZETPPF(P1,2.3) PLOT ZETPPF(P,2.3) FOR X = 0 0.01 0.95
Devroye (1986), "NonUniform Random Variate Generation", SpringerVerlang, New York.
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 alpha = 1.5 title Alpha = ^alpha plot zetppf(p,alpha) for p = 0 0.01 0.99 . let alpha = 2.0 title Alpha = ^alpha plot zetppf(p,alpha) for p = 0 0.01 0.99 . let alpha = 2.5 title Alpha = ^alpha plot zetppf(p,alpha) for p = 0 0.01 0.99 . let alpha = 3.0 title Alpha = ^alpha plot zetppf(p,alpha) for p = 0 0.01 0.99 . end of multiplot . justification center move 50 97 text Zeta Percent Point Functions
Date created: 6/5/2006 