 Dataplot Vol 2 Vol 1

# GL4PDF

Name:
GL4PDF (LET)
Type:
Library Function
Purpose:
Compute the type 4 generalized logistic probability density 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.

Syntax:
LET <y> = GL4PDF(<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 pdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

Examples:
LET A = GL4PDF(3,2,0.5)
LET X2 = GL4PDF(X1,P,Q)
PLOT GL4PDF(X,P,Q) FOR X = -5 0.01 5
Note:
The generalized logistic type 1, type 2, and type 3 distributions are all special cases of the generalized logistic type 4 distribution.
Note:
Generalized logistic type 4 random numbers, probability plots, and goodness of fit tests can be generated with the commands:

LET P = <value>
LET Q = <value>
LET Y = GENERALIZED LOGISTIC TYPE 4 RANDOM NUMBERS ...
FOR I = 1 1 N
GENERALIZED LOGISTIC TYPE 3 PROBABILITY PLOT Y
GENERALIZED LOGISTIC TYPE 3 KOLMOGOROV SMIRNOV ...
GOODNESS OF FIT Y
GENERALIZED LOGISTIC TYPE 3 CHI-SQUARE ...
GOODNESS OF FIT Y

The following commands can be used to estimate the shape parameter for the generalized logistic type 3 distribution:

LET P1 = <value>
LET P2 = <value>
LET Q1 = <value>
LET Q2 = <value>
GENERALIZED LOGISTIC TYPE 4 PPCC PLOT Y
GENERALIZED LOGISTIC TYPE 4 KS PLOT Y

The default values for P1 and P2 are 0.1 and 10, respectively. The default values for Q1 and Q2 are 0.1 and 10, respectively.

Note:
Johnson, Kotz, and Balakrishnan (see Reference section below) also define type 1, type 3, type 4, and a parameterization due to Hoskings generalized logistic distributions. These are also supported by Dataplot (see the Related Commands section below).
Default:
None
Synonyms:
None
Related Commands:
 GL4CDF = Compute the generalized logistic type 4 cumulative distribution 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:
Data Analysis
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 Density
X1LABEL DISPLACEMENT 14
Y1LABEL DISPLACEMENT 15
.
LOOP FOR K = 1 1 3
LET P = PA(K)
LOOP FOR L = 1 1 3
LET Q = QA(L)
TITLE P = ^P, Q = ^Q
PLOT GL4PDF(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 PDF's
``` Date created: 3/27/2006
Last updated: 3/27/2006