Dataplot Vol 2 Vol 1

# GL4PPF

Name:
GL4PPF (LET)
Type:
Library Function
Purpose:
Compute the type 4 generalized logistic percent point 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. The percent point function is then computed by numerically inverting the cumulative distribution function.

Syntax:
LET <y> = GL4PPF(<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 ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

Examples:
LET A = GL4PPF(0.95,2,0.5)
LET X2 = GL4PPF(X1,P,Q)
PLOT GL4PPF(X,P,Q) FOR X = -5 0.01 5
Default:
None
Synonyms:
None
Related Commands:
 GL4CDF = Compute the generalized logistic type 4 cumulative distribution function. GL4PDF = Compute the generalized logistic type 4 probability density 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
Y1LABEL X
X1LABEL Probability
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 GL4PPF(X,P,Q) FOR X = 0.01  0.01  0.99
END OF LOOP
END OF LOOP
END OF MULTIPLOT
CASE ASIS
MOVE 50 97
JUSTIFICATION CENTER
TEXT Generalized Logistic Type 4 PPF's
```

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