Dataplot Vol 2 Vol 1

# GL4CDF

Name:
GL4CDF (LET)
Type:
Library Function
Purpose:
Compute the type 4 generalized logistic cumulative distribution function with shape parameters p and q.
Description:
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.

Syntax:
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.

Examples:
LET A = GL4CDF(3,2,0.5)
LET X2 = GL4CDF(X1,P,Q)
PLOT GL4CDF(X,P,Q) FOR X = -5 0.01 5
Default:
None
Synonyms:
None
Related Commands:
 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.
Reference:
"Continuous Univariate Distributions - 2", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994 (pp. 140-147).
Applications:
Distributional Modeling
Implementation Date:
2006/3
Program:
```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
```

Date created: 3/27/2006
Last updated: 3/27/2006