SLOPPF

SLOPPF (LET)

Library Function

Compute the slope percent point function with shape parameter .

The standard slope distribution has the following percent point function:

with 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

LET <y> = SLOPPF(<p>,<alpha>,<a>,<b>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or variable containing values in the interval (0,1);
            <y> is a variable or a parameter (depending on what <p> is) where the computed slope ppf value is stored;
            <alpha> 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 = SLOPPF(0.95,0.2)
LET Y = SLOPPF(X,0.5,0,5)
PLOT SLOPPF(P,2,0,3) FOR P = 0 0.01 1

None

None

SLOCDF	= Compute the slope cumulative distribution function.
SLOPDF	= Compute the slope probability density function.
TSSPDF	= Compute the two-sided slope probability density function.
OGIPDF	= Compute the ogive probability density function.
TOPPDF	= Compute the Topp and Leone probability density function.
RGTPDF	= Compute the generalized reflected slope probability density function.
GTLPDF	= Compute the generalized slope probability density function.
TSPPDF	= Compute the two-sided power probability density function.
BETPDF	= Compute the alpha probability density function.
TRIPDF	= Compute the triangular probability density function.
TRAPDF	= Compute the trapezoid probability density function.
UNIPDF	= Compute the uniform probability density function.
POWPDF	= Compute the power 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, chapter 8.

Distributional Modeling

2007/10

 
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET ALPHA  = 0.5
TITLE Alpha = ^alpha
PLOT SLOPPF(P,ALPHA) FOR P = 0  0.01  1
.
LET ALPHA  = 1
TITLE Alpha = ^alpha
PLOT SLOPPF(P,ALPHA) FOR P = 0  0.01  1
.
LET ALPHA  = 1.5
TITLE Alpha = ^alpha
PLOT SLOPPF(P,ALPHA) FOR P = 0  0.01  1
.
LET ALPHA  = 2
TITLE Alpha = ^alpha
PLOT SLOPPF(P,ALPHA) FOR P = 0  0.01  1
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Slope Percent Point Functions