GL4CDF

GL4CDF (LET)

Library Function

Compute the type 4 generalized logistic cumulative distribution function with shape parameters p and q.

The standard form of the type 4 generalized logistic distribution has the probability density function:

The general form of the type 4 generalized logistic probability density function can be obtained by replacing x in the above formula with (x-loc)/scale.

The generalized logistic type 4 cumulative distribution function is computed by numerically integrating the probability density function. Dataplot uses the DQAGI routine from the Slatec library to perform the integration.

LET <y> = GL4CDF(<x>,<p>,<q>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, number or parameter;
            <p> is a number or parameter that specifies the value of the first shape parameter;
            <q> is a number or parameter that specifies the value of the second 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 3 cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

LET A = GL4CDF(3,2,0.5)
LET X2 = GL4CDF(X1,P,Q)
PLOT GL4CDF(X,P,Q) FOR X = -5 0.01 5

None

None

GL4PDF	= Compute the generalized logistic type 4 probability density function.
GL4PPF	= Compute the generalized logistic type 4 percent point function.
GLOPDF	= Compute the generalized logistic type 1 probability density function.
GL2PDF	= Compute the generalized logistic type 2 probability density function.
GL3PDF	= Compute the generalized logistic type 3 probability density function.
GL5PDF	= Compute the generalized logistic (Hosking parameterization) probability density function.
LOGPDF	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 PA = DATA 0.5  1  2
LET QA = DATA 0.5  1  2
MULTIPLOT 3 3
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 3
LABEL CASE ASIS
TITLE CASE ASIS
TITLE DISPLACEMENT 2
X1LABEL X
Y1LABEL Probability
X1LABEL DISPLACEMENT 14
Y1LABEL DISPLACEMENT 15
.
LOOP FOR K = 1 1 4
   LET P = PA(K)
   LOOP FOR L = 1 1 3
       LET Q = QA(L)
       TITLE P = ^P, Q = ^Q
       PLOT GL4CDF(X,P,Q) FOR X = -5  0.01  5
   END OF LOOP
END OF LOOP
END OF MULTIPLOT
CASE ASIS
MOVE 50 97
JUSTIFICATION CENTER
TEXT Generalized Logistic Type 4 CDF's