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Dataplot Vol 2 Vol 1

RIGCDF

Name:
    RIGCDF (LET)
Type:
    Library Function
Purpose:
    Compute the reciprocal inverse Gaussian cumulative distribution function with shape parameters gamma and mu.
Description:
    The reciprocal inverse Gaussian distribution is the distribution of (1/X) when X has an inverse Gaussian distribution. It has the following cumulative distribution function:

      F(x;gamma,mu) = NORCDF[-(1/(mu*x) - 1)*SQRT(gamma*x)] - EXP(2/gamma**2)* NORCDF[-(1/(mu*x) - 1)*SQRT(gamma*x)] x >= 0; gamma, mu > 0

    with gamma and mu denoting the shape parameters and NORCDF denoting the cumulative distribution function of the standard normal distribution.

    The reciprocal inverse Gaussian distribution can be computed in terms of the inverse Gaussian distribution by

      RIGCDF(x;gamma,mu) = IGCDF((1/x);gamma,mu)/(x**2)

    The reciprocal inverse Gaussian distribution can be generalized with location and scale parameters in the usual way.

Syntax:
    LET <y> = RIGCDF(<x>,<gamma>,<mu>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable or a parameter;
                <gamma> is number or parameter that specifies the first shape parameter;
                <mu> is number or parameter that specifies the second shape parameter;
                <loc> is number or parameter that specifies the location parameter;
                <scale> is number or parameter that specifies the scale parameter;
                <y> is a variable or a parameter (depending on what <x> is) where the computed reciprocal inverse Gaussian cdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.

    Note that the location and scale parameters are optional.

Examples:
    LET A = RIGCDF(3,2,1)
    LET A = RIGCDF(A1,2,1)
    LET X2 = RIGCDF(X1,2,3)
    PLOT RIGCDF(X,2,1.5) FOR X = 0.1 0.1 5
Default:
    None
Synonyms:
    None
Related Commands:
    RIGCHAZ = Compute the reciprocal inverse Gaussian cumulative hazard function.
    RIGHAZ = Compute the reciprocal inverse Gaussian hazard function.
    RIGPDF = Compute the reciprocal inverse Gaussian probability density function.
    RIGPPF = Compute the reciprocal inverse Gaussian percent point function.
    IGPDF = Compute the reciprocal inverse Gaussian probability density function.
    CHSPDF = Compute the chi-square probability density function.
    FPDF = Compute the F probability density function.
    NORPDF = Compute the normal probability density function.
    TPDF = Compute the t probability density function.
    WEIPDF = Compute the Weibull probability density function.
    WALPDF = Compute the Wald probability density function.
    FLPDF = Compute the fatigue life probability density function.
Reference:
    "Continuous Univariate Distributions--Volume 1", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, chapter 15.

    "Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley, 2000, pp. 114-116.

Applications:
    Distributional Modeling
Implementation Date:
    1990/5: Original implementation
    2003/12: Modified to treat mu as a shape parameter instead of a location parameter.
Program: 
     
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
X1LABEL DISPLACEMENT 12
Y1LABEL DISPLACEMENT 12
MULTIPLOT SCALE FACTOR 2
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
TITLE GAMMA = 2, MU = 1
PLOT RIGCDF(X,2,1) FOR X = 0.01  0.01  5
TITLE GAMMA = 5, MU = 1
PLOT RIGCDF(X,5,1) FOR X = 0.01  0.01  5
TITLE GAMMA = 2, MU = 2
PLOT RIGCDF(X,2,2) FOR X = 0.01  0.01  5
TITLE GAMMA = 5, MU = 2
PLOT RIGCDF(X,5,2) FOR X = 0.01  0.01  5
END OF MULTIPLOT
JUSTIFICATION CENTER
MOVE 50 97
CASE ASIS
TEXT Reciprocal Inverse Gaussian CDF
    plot generated by sample program

Date created: 7/7/2004
Last updated: 7/7/2004
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