SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1

RPOCDF

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

      F(x;c) = 1 - (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

      F(x;c,a,b) = F((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> = RPOCDF(<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 cdf 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 = RPOCDF(0.3,0.2)
    LET Y = RPOCDF(X,0.5,0,5)
    PLOT RPOCDF(X,2.3) FOR X = 0 0.01 1
Default:
    None
Synonyms:
    None
Related Commands:
    RPOPDF = Compute the reflected power probability density function.
    RPOPPF = Compute the reflected power percent point function.
    RPOHAZ = Compute the reflected power hazard function.
    RPOCHAZ = Compute the reflected power cumulative 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 RPOCDF(X,C) FOR X = 0  0.01  1
    .
    LET C  = 1
    TITLE C = ^c
    PLOT RPOCDF(X,C) FOR X = 0  0.01  1
    .
    LET C  = 1.5
    TITLE C = ^c
    PLOT RPOCDF(X,C) FOR X = 0  0.01  1
    .
    LET C  = 2
    TITLE C = ^c
    PLOT RPOCDF(X,C) FOR X = 0  0.01  1
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
    TEXT Reflected Power Cumulative Distribution 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.