RGTCDF

RGTCDF (LET)

Library Function

Compute the reflected generalized Topp and Leone cumulative distribution function with shape parameters and .

The reflected generalized Topp and Leone distribution has the following cumulative distribution function:

with and denoting the shape parameters and a and b the lower and upper limits, respectively.

The case where a = 0 and b = 1 is referred to as the standard reflected generalized Topp and Leone distribution. It has the following cumulative distribution function:

The lower and upper limits are related to the location and scale parameters as follows:

location = a
scale = b - a


Kotz and van Dorp have proposed this distribution as an alternative to the beta distribution. It is distinguished from the beta distribution in that it can have positive density at the lower limit with a strict positive mode.

LET <y> = RGTCDF(<x>,<alpha>,<beta>,<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 generalized Topp and Leone cdf value is stored;
            <alpha> is a number, parameter, or variable in the interval (0, 2) that specifies the first shape parameter;
            <beta> is a positive number, parameter, or variable that specifies the second 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 = RGTCDF(0.3,0.2,1.2)
LET Y = RGTCDF(X,0.5,2)
PLOT RGTCDF(X,2,3) FOR X = 0 0.01 1

None

None

RGTPDF	= Compute the reflected generalized Topp and Leone probability density function.
RGTPPF	= Compute the reflected generalized Topp and Leone percent point function.
GTLPDF	= Compute the generalized Topp and Leone probability density function.
TOPPDF	= Compute the 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	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 7.

Distributional Modeling

2007/2

 
LABEL CASE ASIS
TITLE CASE ASIS
TITLE OFFSET 2
.
MULTIPLOT 3 3
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 3
.
LET ALPHA = 2
LET BETA  = 3
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 6
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 2
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 1.5
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 2
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 0.75
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 0.5
LET BETA  = 0.25
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
LET ALPHA = 1
LET BETA  = 1
TITLE Alpha = ^alpha, Beta = ^beta
PLOT RGTCDF(X,ALPHA,BETA) FOR X = 0  0.01  1
.
END OF MULTIPLOT
.
JUSTIFICATION CENTER
MOVE 50 97
TEXT Reflected Generalized Topp and Leone CDF Functions