RPOCDF

RPOCDF (LET)

Library Function

Compute the reflected power cumulative distribution function with shape parameter c.

The standard reflected power distribution has the following cumulative distribution function:

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

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).

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.

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

None

None

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.

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.

Distributional Modeling

2007/12

 
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
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JUSTIFICATION CENTER
MOVE 50 97
TEXT Reflected Power Cumulative Distribution Functions