GL5CDF

GL5CDF (LET)

Library Function

Compute the type 5 generalized logistic cumulative distribution function with shape parameter .

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 cumulative distribution function:

The general form of the Hosking generalized logistic cumulative distribution function can be obtained by replacing x in the above formula with (x-loc)/scale.

LET <y> = GL5CDF(<x>,<alpha>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, number or parameter;
            <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 <x> is) where the computed generalized logistic type 5 cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

LET A = GL5CDF(-3,2)
LET X2 = GL5CDF(X1,ALPHA)
PLOT GL5CDF(X,2) FOR X = -5 0.01 0.5

None

None

GL5PDF	= Compute the generalized logistic type 5 (Hosking) probability density function.
GL5PPF	= Compute the generalized logistic type 5 (Hosking) percent point 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.

"Continuous Univariate Distributions - 2", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley, 1994 (pp. 140-147).

Distributunial Modeling

2006/3

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
X1LABEL X
Y1LABEL Probability
X1LABEL DISPLACEMENT 12
Y1LABEL DISPLACEMENT 15
.
LOOP FOR K = 1 1 9
   LET ALPHA = A(K)
   LET XSTART = -5
   LET XSTOP = 5
   IF ALPHA > 0
      LET XSTOP = 1/ALPHA
   END OF IF
   IF ALPHA < 0
      LET XSTART = 1/ALPHA
   END OF IF
   TITLE Alpha = ^ALPHA
   PLOT GL5CDF(X,ALPHA) FOR X = XSTART  0.01  XSTOP
END OF LOOP
END OF MULTIPLOT
CASE ASIS
MOVE 50 97
JUSTIFICATION CENTER
TEXT Generalized Logistic Type 5 CDF's