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Dataplot Vol 2 Vol 1

MUTPPF

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

      F(x;beta) = 1 - EXP[-(1/beta)*(EXP(beta*x) - 1) + beta*x]
   0 <= beta <= 1; x > 0

    with beta denoting the shape parameter.

    The percent point function is computed by numerically inverting the cumulative distribution function using a bisection method.

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

      f(x;beta,loc,scale) = (1/scale)*f((x-loc)/scale;beta,0,1)

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

Syntax:
    LET <y> = MUTPPF(<p>,<beta>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a number, parameter, or variable in the interval [0,1];
                <y> is a variable or a parameter (depending on what <p> is) where the computed Muth ppf 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 = MUTPPF(0.95,0.2)
    LET Y = MUTPPF(P,0.5,0,5)
    PLOT MUTPPF(P,0.7,0,3) FOR P = 0.01 0.01 0.99
Default:
    None
Synonyms:
    None
Related Commands:
    MUTCDF = Compute the Muth cumulative distribution function.
    MUTCHAZ = Compute the Muth cumulative hazard function.
    MUTHAZ = Compute the Muth hazard function.
    MUTPDF = Compute the Muth probability density 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 MUTPPF(P,BETA) FOR P = 0.01  0.01  0.99
    .
    LET BETA  = 0.5
    TITLE BETA = ^BETA
    PLOT MUTPPF(P,BETA) FOR P = 0.01  0.01  0.99
    .
    LET BETA  = 0.7
    TITLE BETA = ^BETA
    PLOT MUTPPF(P,BETA) FOR P = 0.01  0.01  0.99
    .
    LET BETA  = 1
    TITLE BETA = ^BETA
    PLOT MUTPPF(P,BETA) FOR P = 0.01  0.01  0.99
    .
    END OF MULTIPLOT
    .
    JUSTIFICATION CENTER
    MOVE 50 97
    TEXT Muth Percent Point 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.