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PARPDFName:
with and a denoting the tail length shape parameter and the lower bound parameter, respectively. The default value of a is 1. Note that although the a parameter is typically called a location parameter (and it is in the sense that it defines the lower bound), it is not a location parameter in the technical sense that the following relation does not hold:
For this reason, Dataplot treats a as a shape parameter. In Dataplot, the a shape parameter is optional with a default value of 1.
<SUBSET/EXCEPT/FOR qualification> where <x> is a variable, a number, or a parameter; <gamma> is a number or parameter that specifies the tail length shape parameter; <a> is a number or parameter that specifies the optional lower bound shape parameter; <loc> is a number or parameter that specifies the optional location parameter; <scale> is a number or parameter that specifies the optional scale parameter; <y> is a variable or a parameter (depending on what <x> is) where the computed Pareto pdf value is saved; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The a, loc, and scale parameters are all optional.
LET A = PARPDF(3,1.5,2) LET Y = PARPDF(X,GAMMA,A,LOC,SCALE)
Most applications of the Pareto distribution use the standard form (i.e., location = 0 and scale = 1).
LET A = <value> LET Y = PARETO RANDOM NUMBERS FOR I = 1 1 N PARETO PROBABILITY PLOT Y PARETO KOLMOGOROV SMIRNOV GOODNESS OF FIT Y PARETO CHI-SQUARE GOODNESS OF FIT Y The following commands can be used to estimate the shape parameters for the Pareto distribution:
LET GAMMA2 = <value> LET A = <value> PARETO PPCC PLOT Y PARETO KS PLOT Y The default values for gamma1 and gamma2 are 0.2 and 10, respectively. Note that only the gamma parameter is estimated for these plots. The default value of A is 1. If the value of A is greater than the data minimum, then it is automatically set to the data minimum. You can generate maximum likelihood estimates for the Pareto distribution with the command
The maximum likelihood estimate of the lower bound parameter is:
This estimate is used in the following equation to find the maximum likelihood estimate of the tail length parameter:
MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 . CASE ASIS TITLE CASE ASIS LABEL CASE ASIS TITLE DISPLACEMENT 2 Y1LABEL DISPLACEMENT 15 X1LABEL DISPLACEMENT 12 Y1LABEL Probability Density X1LABEL X . TITLE Gamma = 1 PLOT PARPDF(X,1) FOR X = 1 0.1 10 TITLE Gamma = 2 PLOT PARPDF(X,2) FOR X = 1 0.1 10 TITLE Gamma = 5 PLOT PARPDF(X,5) FOR X = 1 0.1 10 TITLE Gamma = 0.5 PLOT PARPDF(X,0.5) FOR X = 1 0.1 10 END OF MULTIPLOT . MOVE 50 97 JUSTIFICATION CENTER TEXT Pareto PDF Functions
Date created: 8/23/2006 |