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Dataplot Vol 2 Vol 1

LEXCHAZ

Name:
    LEXCHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the logistic-exponential cumulative hazard function with shape parameter beta.
Description:
    The standard logistic-exponential distribution has the following cumulative hazard function:

      H(x;beta) = -LOG(1/[1 + EXP(x) -1)**beta])    beta, x > 0

    with beta denoting the shape parameter.

    This distribution can be generalized with location and scale parameters in the usual way using the relation

      H(x;beta,mu,alpha) = H((x-mu)/alpha;beta,0,1)

    with mu and alpha denoting the location and scale parameters, respectively.

Syntax:
    LET <y> = LEXCHAZ(<x>,<beta>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, parameter, or variable;
                <y> is a variable or a parameter (depending on what <x> is) where the computed logistic-exponential cumulative hazard value is stored;
                <beta> is a number, parameter, or variable that specifies the shape parameter;
                <loc> is a number, parameter, or variable that specifies the location parameter;
                <scale> is a positive number, parameter, or variable that specifies the scale parameter;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    If <loc> and <scale> are omitted, they default to 0 and 1, respectively.

Examples:
    LET A = LEXCHAZ(0.3,0.2)
    LET Y = LEXCHAZ(X,0.5,0,5)
    PLOT LEXCHAZ(X,0.7,0,3) FOR X = 0 0.01 5
Default:
    None
Synonyms:
    None
Related Commands:
    LEXCDF = Compute the logistic-exponential cumulative distribution function.
    LEXHAZ = Compute the logistic-exponential hazard function.
    LEXPDF = Compute the logistic-exponential probability density function.
    LEXPPF = Compute the logistic-exponential percent point function.
    RAYPDF = Compute the Rayleigh probability density function.
    WEIPDF = Compute the Weibull probability density function.
    LGNPDF Compute the lognormal probability density function.
    EXPPDF = Compute the exponential probability density function.
    LOGPDF = Compute the logistic probability density function.
    GAMPDF = Compute the gamma probability density function.
    EWEPDF = Compute the exponentiated Weibull probability density function.
    B10PDF = Compute the Burr type 10 probability density function.
Reference:
    Leemis and McQuestion (2008), "Univariate Distribution Relationships", The American Statistician, Vol. 62, No. 1, pp. 45-53.

    Lan and Leemis (2008), "The Logistic-Exponential Survival Distribution", Naval Research Logistics, to appear.

Applications:
    Distributional Modeling
Implementation Date:
    2008/2
Program:
     
    LABEL CASE ASIS
    TITLE CASE ASIS
    TITLE OFFSET 2
    .
    MULTIPLOT 2 2
    MULTIPLOT CORNER COORDINATES 0 0 100 95
    MULTIPLOT SCALE FACTOR 2
    .
    LET BETA  = 0.5
    TITLE BETA = ^BETA
    PLOT LEXCHAZ(X,BETA) FOR X = 0.01  0.01  5
    .
    LET BETA  = 1
    TITLE BETA = ^BETA
    PLOT LEXCHAZ(X,BETA) FOR X = 0.01  0.01  5
    .
    LET BETA  = 2
    TITLE BETA = ^BETA
    PLOT LEXCHAZ(X,BETA) FOR X = 0.01  0.01  5
    .
    LET BETA  = 5
    TITLE BETA = ^BETA
    PLOT LEXCHAZ(X,BETA) FOR X = 0.01  0.01  5
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
    TEXT Logistic-Exponential Cumulative Hazard Functions
        
    plot generated by sample program

Date created: 2/14/2008
Last updated: 2/14/2008
Please email comments on this WWW page to alan.heckert@nist.gov.