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Dataplot Vol 2 Vol 1

POWCHAZ

Name:
    POWCHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the power function cumulative hazard function with shape parameter c.
Description:
    The standard form of the cumulative hazard function is:

      H(x,c) = -LOG(1-x**c)      0 <= x < 1; c > 0

    with c denoting the shape parameter.

    This distribution can be extended with lower and upper bound parameters. If a and b denote the lower and upper bounds, respectively, then the location and scale parameters are:

      location = a
      scale = b - a

    The general form of the distribution can then be found by using the relation

      H(x;c,a,b) = H((x-a)/(b-a);c,0,1)

    If X has a Pareto distribution, then 1/X has a power distribution. The power distribution is also a special case of the beta distribution where the second shape parameter is equal to 1 (the reflected power distribution is the special case of the beta distribution where the first shape parameter = 1).

Syntax:
    LET <y> = POWCHAZ(<x>,<c>,<a>,<b>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, parameter, or variable containing values in the interval (a,b);
                <y> is a variable or a parameter (depending on what <x> is) where the computed power cumulative hazard value is stored;
                <c> is a positive number, parameter, or variable that specifies the shape parameter;
                <a> is a number, parameter, or variable that specifies the lower limit;
                <b> is a number, parameter, or variable that specifies the upper limit;
                and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    If <a> and <b> are omitted, they default to 0 and 1, respectively.

Examples:
    LET A = POWCHAZ(3,1.5)
    LET X2 = POWCHAZ(X1,C)
Default:
    None
Synonyms:
    None
Related Commands:
    POWPDF = Compute the power probability density function.
    POWCDF = Compute the power cumulative distribution function.
    POWPPF = Compute the power percent point function.
    POWCHAZ = Compute the power hazard function.
    RPOPDF = Compute the reflected power probability density function.
    BETPDF = Compute the beta probability density function.
    TOPPDF = Compute the Topp and Leone probability density function.
    RGTPDF = Compute the generalized reflected Topp and Leone probability density function.
    GTLPDF = Compute the generalized Topp and Leone probability density function.
    TSPPDF = Compute the two-sided power probability density function.
    TRIPDF = Compute the triangular probability density function.
    TRAPDF = Compute the trapezoid probability density function.
    UNIPDF = Compute the uniform probability density function.
    JSBPDF = Compute the Johnson SB probability density function.
Reference:
    Johnson, Kotz, and Balakrishnan (1994), "Continuous Univariate Distributions--Volume 1", Second Edition, John Wiley and Sons, p. 607.

    Evans, Hastings, and Peacock (2000), "Statistical Distributions", Third Edition, John Wiley & Sons, chapter 33.

Applications:
    Distributional Modeling
Implementation Date:
    2007/12
Program:
     
    TITLE POWER FUNCTION CUMULATIVE HAZARD FUNCTIONS (0.1,  0.5, 1, 3, 10)
    PLOT POWCHAZ(X,0.1) FOR X = 0.01 0.01 0.99 AND
    PLOT POWCHAZ(X,0.5) FOR X = 0.01 0.01 0.99 AND
    PLOT POWCHAZ(X,1) FOR X = 0.01 0.01 0.99 AND
    PLOT POWCHAZ(X,2) FOR X = 0.01 0.01 0.99 AND
    PLOT POWCHAZ(X,5) FOR X = 0.01 0.01 0.99
        
    plot generated by sample program

Date created: 12/17/2007
Last updated: 12/17/2007
Please email comments on this WWW page to alan.heckert@nist.gov.