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

MUTHAZ

Name:
    MUTHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the Muth hazard function with shape parameter beta.
Description:
    The standard Muth distribution has the following hazard function:

      h(x;beta) = EXP(beta*x) - beta    0 <= beta <= 1; 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,loc,scale) = (1/scale)*h((x-loc)/scale;beta,0,1)

    with <loc> and <scale> denoting the location and scale parameters, respectively.

Syntax:
    LET <y> = MUTHAZ(<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 Muth 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 = MUTHAZ(0.3,0.2)
    LET Y = MUTHAZ(X,0.5,0,5)
    PLOT MUTHAZ(X,0.7,0,3) FOR X = 0 0.01 5
Default:
    None
Synonyms:
    None
Related Commands:
    MUTCDF = Compute the Muth cumulative distribution function.
    MUTCHAZ = Compute the Muth cumulative hazard function.
    MUTPDF = Compute the Muth probability density function.
    MUTPPF = Compute the Muth 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.

    Muth (1977), "Reliability Models with Positive Memory Derived from the Mean Residual Life Function", in The Theory and Applications of Reliability, Eds. Tsokos and Shimi, New York: Academic Press Inc., pp. 401-435.

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  = 0.2
    TITLE BETA = ^BETA
    PLOT MUTHAZ(X,BETA) FOR X = 0.01  0.01  5
    .
    LET BETA  = 0.5
    TITLE BETA = ^BETA
    PLOT MUTHAZ(X,BETA) FOR X = 0.01  0.01  5
    .
    LET BETA  = 0.7
    TITLE BETA = ^BETA
    PLOT MUTHAZ(X,BETA) FOR X = 0.01  0.01  5
    .
    LET BETA  = 1
    TITLE BETA = ^BETA
    PLOT MUTHAZ(X,BETA) FOR X = 0.01  0.01  5
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
    TEXT Muth 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.