GL2CDF

GL2CDF (LET)

Library Function

Compute the type 2 generalized logistic cumulative distribution function with shape parameter .

The standard form of the type 2 generalized logistic distribution has the cumulative distribution function:

The general form of the type 2 generalized logistic cumulative distribution function can be obtained by replacing x in the above formula with (x-loc)/scale.

LET <y> = GL2CDF(<x>,<alpha>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, number or parameter;
            <alpha> is a number or parameter that specifies the value of the shape parameter;
            <loc> is a number or parameter that specifies the value of the location parameter;
            <scale> is a number or parameter that specifies the value of the scale parameter;
            <y> is a variable or a parameter (depending on what <x> is) where the computed generalized logistic type 2 cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

LET A = GL2CDF(3,2)
LET X2 = GL2CDF(X1,ALPHA)
PLOT GL2CDF(X,ALPHA) FOR X = -5 0.01 5

None

None

GL2PDF	= Compute the generalized logistic type 2 probability density function.
GL2PPF	= Compute the generalized logistic type 2 percent point function.
GLOPDF	= Compute the generalized logistic type 1 probability density function.
GL3PDF	= Compute the generalized logistic type 3 probability density function.
GL4PDF	= Compute the generalized logistic type 4 probability density function.
GL5PDF	= Compute the generalized logistic (Hosking parameterization) probability density function.
LOGPDF	= Compute the logistic probability density function.
NORPDF	= Compute the normal probability density function.
LGNPDF	= Compute the logmormal probability density function.

"Continuous Univariate Distributions - 2", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994 (pp. 140-147).

Distributional Modeling

2006/3

 
LET A = DATA 0.5  1  2  5
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
LABEL CASE ASIS
TITLE CASE ASIS
TITLE DISPLACEMENT 2
X1LABEL X
Y1LABEL Probability
X1LABEL DISPLACEMENT 12
Y1LABEL DISPLACEMENT 15
.
LOOP FOR K = 1 1 4
   LET ALPHA = A(K)
   TITLE Alpha = ^ALPHA
   PLOT GL2CDF(X,ALPHA) FOR X = -5  0.01  5
END OF LOOP
END OF MULTIPLOT
CASE ASIS
MOVE 50 97
JUSTIFICATION CENTER
TEXT Generalized Logistic Type 2 CDF's