TSSCDF

TSSCDF (LET)

Library Function

Compute the two-sided slope cumulative distribution function with shape parameters and .

The standard two-sided slope distribution has the following cumulative distribution function:

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> = TSSCDF(<x>,<alpha>,<theta>,<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 two-sided slope cdf value is stored;
            <alpha> is a number, parameter, or variable in the interval (0,2) that specifies the first shape parameter;
            <theta> is a number, parameter, or variable in the interval (a,b) that specifies the second shape parameter;
            <a> is a number, parameter, or variable that specifies the lower bound;
            <b> is a number, parameter, or variable that specifies the upper bound;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

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

LET A = TSSCDF(0.3,1.2,0.3)
LET Y = TSSCDF(X,1.5,2.2,0,5)
PLOT TSSCDF(X,1.5,2.2,0,5) FOR X = 0 0.01 5

None

None

TSSPDF	= Compute the two-sided slope probability density function.
TSSPPF	= Compute the two-sided slope percent point function.
SLOPDF	= Compute the slope probability density function.
OGIPDF	= Compute the ogive probability density function.
TSOPDF	= Compute the two-sided ogive 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.
BETPDF	= Compute the beta 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

MULTIPLOT 3 3
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 3
TITLE OFFSET 2
TITLE CASE ASIS
LABEL CASE ASIS
CASE ASIS
.
LET THETAV = DATA 0.25  0.50 0.75
LET ALPHAV = DATA 0.5  1.0  1.5
.
LOOP FOR K = 1 1 3
   LET THETA = THETAV(K)
   LOOP FOR L = 1 1 3
      LET ALPHA = ALPHAV(L)
      TITLE Theta = ^THETA, Alpha = ^ALPHA
      PLOT TSSCDF(X,ALPHA,THETA) FOR X = 0  0.01  1
   END OF LOOP
END OF LOOP
.
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT Two-Sided Slope Cumulative Distribution Functions