Dataplot Vol 2 Vol 1

# GL5PPF

Name:
GL5PPF (LET)
Type:
Library Function
Purpose:
Compute the type 5 generalized logistic percent point function with shape parameter .
Description:
Johnson, Kotz, and Balakrishnan (see Reference Section below) define five different versions of the generalized logistic distribution. The first four are referred to as type 1, type 2, type 3, and type 4. The fifth is a version used by Hosking. Although they do not give this version a specific name, Dataplot refers to it as either the generalized logistic type 5 or the Hosking generalized logistic distribution.

The standard form of the Hosking generalized logistic distribution has the percent point function:

The general form of the Hosking generalized logistic percent point function can be obtained from the relation

G(p; , loc,scale) = loc + scale*G(p; )
Syntax:
LET <y> = GL5PPF(<p>,<alpha>,<loc>,<scale>)
<SUBSET/EXCEPT/FOR qualification>
where <p> is a variable, number or parameter in the range (0,1);
<alpha> is a number or parameter that specifies the value of the first 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 <p> is) where the computed generalized logistic type 5 ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

Examples:
LET A = GL5PPF(0.95,0.5)
LET X2 = GL5PPF(P1,ALPHA)
PLOT GL5PPF(P,0.22) FOR P = 0.01 0.01 0.99
Default:
None
Synonyms:
None
Related Commands:
 GL5CDF = Compute the generalized logistic type 5 (Hosking) cumulative distribution function. GL5PDF = Compute the generalized logistic type 5 (Hosking) probability density function. GLOPDF = Compute the generalized logistic type 1 probability density function. GL2PDF = Compute the generalized logistic type 2 probability density function. GL43DF = Compute the generalized logistic type 3 probability density function. GL4PDF = Compute the generalized logistic type 4 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:
Distributunial Modeling
Implementation Date:
2006/3
Program:
```LET A = DATA -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1
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 12
Y1LABEL DISPLACEMENT 15
.
LOOP FOR K = 1 1 9
LET ALPHA = A(K)
LET XSTART = 0.01
LET XSTOP = 0.99
IF ALPHA > 0
LET XSTOP = 1
END OF IF
IF ALPHA < 0
LET XSTART = 0
END OF IF
TITLE Alpha = ^ALPHA
PLOT GL5PPF(P,ALPHA) FOR P = XSTART  0.01  XSTOP
END OF LOOP
END OF MULTIPLOT
CASE ASIS
MOVE 50 97
JUSTIFICATION CENTER
TEXT Generalized Logistic Type 5 PPF's
```

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