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BGEPPFName:
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![]() ![]() The beta-geometric distribution has the following probability density function:
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with Dataplot computes the cumulative distribution function using a recurrence relation given by Hesselager. Hesselager gives the recurrence relation as:
![]() Converting this to the parameterization above yields
![]() Dataplot computes the percent point function by summing the cumulative distribution function until the specified probability is obtained.
<SUBSET/EXCEPT/FOR qualification> where <p> is a number, parameter, or variable in the interval (0,1); <alpha> is a number, parameter, or variable that specifies the first shape parameter; <beta> is a number, parameter, or variable that specifies the second shape parameter; <y> is a variable or a parameter (depending on what <p> is) where the computed beta-geometric ppf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = BGEPPF(P,2.1,4) PLOT BGEPPF(P,ALPHA,BETA) FOR P = 0 0.01 0.99
![]() We will refer to the first parameterization as the unshifted parameterization and the second parameterization as the shifted parameterization. To specify the shifted parameterization (i.e., starting at x = 0), enter the command
To reset the unshifted parameterization (i.e., starting at x = 1), enter the command
This distribution is also sometimes given with
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Irwin developed the Waring distribution based on the Waring expansion. The probability mass function for the Waring distribution is
![]() The Waring distribution can be computed with the shifted form of the beta-geometric distribution with the following change in parameters:
![]() ![]() If a = 1, then the Waring distribution reduces to the Yule distribution. You can compute the Waring (and Yule) percent point functions using the BGEPPF routine with the above re-parameterization or you can use the WARPPF or YULPPF routines directly (enter HELP WARPDF or HELP YULPDF for details).
XLIMITS 0 1 XTIC OFFSET 0.5 0.5 . TITLE CASE ASIS LABEL CASE ASIS Y1LABEL Number of Successes X1LABEL Probability TITLE DISPLACEMENT 2 Y1LABEL DISPLACEMENT 15 X1LABEL DISPLACEMENT 12 . MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 . TITLE Alpha = 0.5, Beta = 0.5 PLOT BGEPPF(P,0.5,0.5) FOR P = 0 0.01 0.99 . TITLE Alpha = 3, Beta = 0.5 PLOT BGEPPF(P,3.0,0.5) FOR P = 0 0.01 0.99 . TITLE Alpha = 0.5, Beta = 3 PLOT BGEPPF(P,0.5,3.0) FOR P = 0 0.01 0.99 . TITLE Alpha = 3, Beta = 3 PLOT BGEPPF(P,3.0,3.0) FOR P = 0 0.01 0.99 . END OF MULTIPLOT . CASE ASIS JUSTIFICATION CENTER MOVE 50 97 TEXT Beta-Geometric Percent Point Functions ![]()
Date created: 8/23/2006 |