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Dataplot Vol 2 Vol 1

YULCDF

Name:
    YULCDF (LET)
Type:
    Library Function
Purpose:
    Compute the Yule cumulative distribution function.
Description:
    The Yule distribution has the following cumulative distribution function:

      F(x,p) = SUM[i=0 to x][p*p!*i!/(i+p+1)! p] > 0, x = 0, 1, 2, ... = SUM[i=0 to x][p*GAMMA(p+1)*GAMMA(i+1)/GAMMA(i+p+2)]

    with p denoting the shape parameter and GAMMA denoting the gamma function (HELP GAMMA for details).

    Dataplot computes the Yule cumulative distribution function using the above sum. The individual terms are computed using the log gamma function. The Yule distribution has increasingly long tails as p goes to zero. Currently, Dataplot limits the Yule pdf function to the case where p >= 0.1.

Syntax:
    LET <y> = YULCDF(<x>,<p>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a non-negative integer number, parameter, or variable;
                <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 cdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = YULCDF(3,1.5)
    LET A = YULCDF(X,P)
    PLOT YULCDF(X,2) FOR X = 0 1 50
Note:
    The Yule is a special case of the Waring distribution. Specifically,

      YULPDF(X,P) = WARPDF(X,P-1,1)
Default:
    None
Synonyms:
    None
Related Commands:
    YULPDF = Compute the Yule probability mass function.
    YULPPF = Compute the Yule percent point function.
    WARPDF = Compute the Waring probability density function.
    BBNPDF = Compute the beta-binomial probability density function.
    GEOPDF = Compute the geometric probability density function.
    NBPDF = Compute the negative binomial probability density function.
    HYPPDF = Compute the hypergeometric probability density function.
Reference:
    "Discrete Univariate Distributions", Second Edition, Johnson, Kotz, and Kemp, John Wiley & Sons, 1994 (pp. 274-279).
Applications:
    Distributional Modeling
Implementation Date:
    2004/4
Program: 
     
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
X1LABEL DISPLACEMENT 12
Y1LABEL DISPLACEMENT 12
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
XTIC OFFSET 0.5 0.5
LINE BLANK
SPIKE ON
TITLE AUTOMATIC
X1LABEL X
Y1LABEL PROBABILITY
TITLE SIZE 3
PLOT YULCDF(X,0.5) FOR X = 0 1 50
PLOT YULCDF(X,1) FOR X = 0 1 50
PLOT YULCDF(X,1.5) FOR X = 0 1 50
PLOT YULCDF(X,2) FOR X = 0 1 50
END OF MULTIPLOT
    plot generated by sample program

Date created: 7/7/2004
Last updated: 7/7/2004
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