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Dataplot Vol 2 Vol 1

PARCHAZ

Name:
    PARCHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the Pareto cumulative hazard function with shape parameters gamma and a.
Description:
    The standard form of the Pareto cumulative hazard function is:

      H(x;gamma,a) = gamma*LOG(x/a) x >= a; a, gamma > 0

    with gamma 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:

      H(x;gamma,a) = f((x-a);gamma,0)

    with H denoting the cumulative hazard 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.

Syntax:
    LET <y> = PARCHAZ(<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 cumulative hazard value is saved;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

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

Examples:
    LET A = PARCHAZ(3,1.5)
    LET A = PARCHAZ(3,1.5,2)
    LET Y = PARCHAZ,GAMMA,A,LOC,SCALE)
    PLOT PARCHAZ(X,GAMMA,A,LOC,SCALE) FOR X = XSTART 0.01 XSTOP
Note:
    The Pareto cumulative hazard function can be extended with location and scale parameters by using the relationship

      H(x;gamma,a,loc,scale) = H((x-loc)/scale;gamma,a,0,1)

    Most applications of the Pareto distribution use the standard form (location = zero, scale = one).

Default:
    None
Synonyms:
    None
Related Commands:
    PARCDF = Compute the Pareto cumulative distribution 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.
Reference:
    "Continuous Univariate Distributions: Volume 1", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 19.
Applications:
    Distributional Modeling
Implementation Date:
    1998/4
Program: 
     
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 Cumulative Hazard
X1LABEL X
.
TITLE Gamma = 1
PLOT PARCHAZ(X,1) FOR X = 1 0.1 10
TITLE Gamma = 2
PLOT PARCHAZ(X,2) FOR X = 1 0.1 10
TITLE Gamma = 5
PLOT PARCHAZ(X,5) FOR X = 1 0.1 10
TITLE Gamma = 0.5
PLOT PARCHAZ(X,0.5) FOR X = 1 0.1 10
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT Pareto Cumulative Hazard Functions
    plot generated by sample program

Date created: 8/23/2006
Last updated: 8/23/2006
Please email comments on this WWW page to alan.heckert@nist.gov.