PARCDF

PARCDF (LET)

Library Function

Compute the Pareto cumulative distribution function with shape parameters and a.

The standard form of the Pareto cumulative distrubution function is:

with and a denoting the tail length shape parameter and the lower bound parameter, respectively.

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:

with F denoting the cumulative distribution function.

For this reason, Dataplot treats a as a shape parameter. In Dataplot, the a shape parameter is optional with a default value of 1.

LET <y> = PARCDF(<x>,<gamma>,<a>,<loc>,<scale>)
                        <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 cdf value is saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The a, loc, and scale parameters are all optional.

LET A = PARCDF(3,1.5)
LET A = PARCDF(3,1.5,2)
LET Y = PARCDF(X,GAMMA,A,LOC,SCALE)
PLOT PARCDF(X,GAMMA,A,LOC,SCALE) FOR X = XSTART 0.01 XSTOP

The Pareto cumulative distribution can be extended with location and scale parameters by using the relationship

Most applications of the Pareto distribution use the standard form (i.e., location = 0 and scale = 1).

None

None

PARCHAZ	= Compute the Pareto cumulative hazard function.
PARHAZ	= Compute the Pareto hazard function.
PARPDF	= Compute the Pareto probability density function.
PARPPF	= Compute the Pareto percent point function.
GEPPDF	= Compute the generalized Pareto probability density function.
EV1PDF	= Compute the extreme value type I probability density function.
WEIPDF	= Compute the Weibull probability density function.
EXPPDF	= Compute the exponential probability density function.

"Continuous Univariate Distributions: Volume 1", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 19.

Distributional Modeling

1994/4

 
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
X1LABEL X
.
TITLE Gamma = 1
PLOT PARCDF(X,1) FOR X = 1 0.1 10
TITLE Gamma = 2
PLOT PARCDF(X,2) FOR X = 1 0.1 10
TITLE Gamma = 5
PLOT PARCDF(X,5) FOR X = 1 0.1 10
TITLE Gamma = 0.5
PLOT PARCDF(X,0.5) FOR X = 1 0.1 10
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT Pareto CDF Functions