Dataplot Vol 2 Auxiliary Chapter

WEIHAZ

Name:
    WEIHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the Weibull hazard function with tail length parameter gamma.
Description:
    For the minimum order statistic, the standard form of the Weibull hazard function is:

      h(x,gamma) = gamma*x**(gamma - 1)     x > 0, gamma > 0

    For the maximum order statistic, the standard form of the Weibull hazard function is:

      h(x,gamma) = gamma*(-x)**(gamma - 1)  x < 0, gamma > 0
Syntax:
    LET <y> = WEIHAZ(<x>,<gamma>,<loc>, <scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable, number, or parameter;
                  <y> is a variable or a parameter (depending on what <x> is) where the computed Weibull hazard value is stored;
                  <gamma> is a positive number, parameter, or variable that specifies the tail length parameter;
                  <loc> is a positive number, parameter, or variable that specifies the location parameter;
                  <scale> is a positive number, parameter, or variable that specifies the scale parameter;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    The location and scale parameters are optional.

Examples:
    LET A = WEIHAZ(3,2)
    LET Y = WEIHAZ(X,4)
    LET Y = WEIHAZ(X,2,0,5)
    PLOT WEIHAZ(X,2) FOR X = 0.01 0.01 10
Note:
    The SET MINMAX command specifies whether the minimum or maximum order statistic form is used. Entering SET MINMAX 2 specifies the maximum order statistic while entering SET MINMAX specifies the minimum order statistic.
Note:
    For the minimum order statistic, the general form of the Weibull hazard function is:

      h(x,gamma,u,beta) = gamma*(x-u)**(gamma - 1)/(beta**gamma)   x > u, gamma > 0, beta > 0

    For the maximum order statistic, the general form of the Weibull probability density function is:

      h(x,gamma,u,beta) = gamma*(-(-x-u))**(gamma - 1)/(beta**gamma)   x < u, gamma > 0, beta > 0

    where u is the location parameter and beta is the is the scale parameter.

Default:
    None
Synonyms:
    None
Related Commands:
    WEICHAZ = Compute the Weibull cumulative hazard function.
    WEICDF = Compute the Weibull cumulative distribution function.
    WEIPDF = Compute the Weibull probability density function.
    WEIPPF = Compute the Weibull percent point function.
    EXPHAZ = Compute the exponential cumulative hazard function.
    EV1HAZ = Compute the extreme value type I hazard function.
    EV2HAZ = Compute the extreme value type II hazard function.
    LGNHAZ = Compute the lognormal hazard function.
Reference:
    "Continuous Univariate Distributions--Vol. I", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley and Sons, 1994.

    "Statistical Distributions", 2nd. Edition, Evans, Hastings, and Peacock, Wiley and Sons, 1993 (chapter 18).

Applications:
    Reliability Analysis
Implementation Date:
    1998/5
Program:
    MULTIPLOT 2 2
    MULTIPLOT CORNER COORDINATES 0 0 100 100
    SET MINMAX 1
    X1LABEL GAMMA = 1
    PLOT WEIHAZ(X,1) FOR X = 0.01 0.01 3
    X1LABEL GAMMA = 2
    PLOT WEIHAZ(X,2) FOR X = 0.01 0.01 3
    X1LABEL GAMMA = 5
    PLOT WEIHAZ(X,5) FOR X = 0.01 0.01 3
    X1LABEL GAMMA = 0.5
    PLOT WEIHAZ(X,0.5) FOR X = 0.01 0.01 3
    END OF MULTIPLOT
    MOVE 50 97
    JUSTIFICATION CENTER
    TEXT WEIBULL HAZARD PLOTS

    plot generated by sample program

Date created: 6/5/2001
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.