OGIPPF

OGIPPF (LET)

Library Function

Compute the ogive percent point function with shape parameter n.

The standard ogive distribution has the following probability density function:

with n denoting the shape parameter.

The cumulative distribution function is computed by numerically integrating the probability density function. The percent point function is computed by numerically inverting the 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> = OGIPPF(<p>,<n>,<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 ogive ppf value is stored;
            <n> 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 = OGIPPF(0.05,2.2)
LET Y = OGIPPF(P,2.5,0,5)
PLOT OGIPPF(P,2,0,3) FOR P = 0 0.01 1

None

None

OGICDF	= Compute the ogive cumulative distribution function.
OGPPDF	= Compute the ogive probability density function.
TSOPDF	= Compute the two-sided ogive probability density function.
SLOPDF	= Compute the slope probability density function.
TSSPDF	= Compute the two-sided slope 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

 
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
.
LET N  = 0.5
TITLE N = ^n
PLOT OGIPPF(P,N) FOR P = 0  0.01  1
.
LET N  = 0.8
TITLE N = ^n
PLOT OGIPPF(P,N) FOR P = 0  0.01  1
.
LET N  = 1.5
TITLE N = ^n
PLOT OGIPPF(P,N) FOR P = 0  0.01  1
.
LET N  = 2
TITLE N = ^n
PLOT OGIPPF(P,N) FOR P = 0  0.01  1
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Ogive Cumulative Distribution Functions