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Dataplot Vol 2 Vol 1

RPOCHAZ

Name:
    RPOCHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the reflected power cumulative hazard function with shape parameter c.
Description:
    The standard reflected power distribution has the following cumulative hazard function:

      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)

    The reflected power distribution is a special case of the beta distribution where the first shape parameter = 1 (the power distribution is a special case of the beta distribution where the second shape parameter = 1).

Syntax:
    LET <y> = RPOCHAZ(<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 reflected 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 = RPOCHAZ(0.3,0.2)
    LET Y = RPOCHAZ(X,0.5,0,5)
    PLOT RPOCHAZ(X,2.3) FOR X = 0 0.01 0.99
Default:
    None
Synonyms:
    None
Related Commands:
    RPOPDF = Compute the reflected power probability density function.
    RPOCDF = Compute the reflected power cumulative distribution function.
    RPOPPF = Compute the reflected power percent point function.
    RPOHAZ = Compute the reflected power hazard function.
    POWPDF = Compute the 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:
    Samuel Kotz and J. Rene Van Dorp 2004, "Beyond Beta: Other Continuous Families of Distributions with Bounded Support and Applications", World Scientific, pp. 199-201.
Applications:
    Distributional Modeling
Implementation Date:
    2007/12
Program:
     
    LABEL CASE ASIS
    TITLE CASE ASIS
    TITLE OFFSET 2
    .
    MULTIPLOT 2 2
    MULTIPLOT CORNER COORDINATES 0 0 100 95
    MULTIPLOT SCALE FACTOR
    .
    LET C  = 0.5
    TITLE C = ^c
    PLOT RPOCHAZ(X,C) FOR X = 0  0.01  0.99
    .
    LET C  = 1
    TITLE C = ^c
    PLOT RPOCHAZ(X,C) FOR X = 0  0.01  0.99
    .
    LET C  = 1.5
    TITLE C = ^c
    PLOT RPOCHAZ(X,C) FOR X = 0  0.01  0.99
    .
    LET C  = 2
    TITLE C = ^c
    PLOT RPOCHAZ(X,C) FOR X = 0  0.01  0.99
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
    TEXT Reflected Power Cumulative Hazard Functions
        
    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.