SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1

GL5CDF

Name:
    GL5CDF (LET)
Type:
    Library Function
Purpose:
    Compute the type 5 generalized logistic cumulative distribution function with shape parameter alpha.
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 cumulative distribution function:

      F(x;alpha) = 1/(1 + (1 - alpha*x)**(1/alpha))   
x <= 1/alpha  when alpha > 0   x >= 1/alpha  when alpha < 0

    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.

Syntax:
    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.

Examples:
    LET A = GL5CDF(-3,2)
    LET X2 = GL5CDF(X1,ALPHA)
    PLOT GL5CDF(X,2) FOR X = -5 0.01 0.5
Default:
    None
Synonyms:
    None
Related Commands:
    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.
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
    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
        
    plot generated by sample program

Date created: 3/27/2006
Last updated: 3/27/2006
Please email comments on this WWW page to alan.heckert@nist.gov.