RIGPPF

RIGPPF (LET)

Library Function

Compute the reciprocal inverse Gaussian percent point function with shape parameters gamma and mu.

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:

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

The percent point function is the inverse of the cumulative distribution function. The percent point function for the reciprocal inverse Gaussian distribution does not exist in simple, closed form.

The reciprocal inverse Gaussian percent point function can be computed in terms of the inverse Gaussian percent point function by

with IGPPF denoting the percent point function of the inverse Gaussian distribution.

Dataplot uses this relationship to compute the reciprocal inverse gaussian percent point function.

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

LET <y> = RIGCHAZ(<p>,<gamma>,<mu>,<loc>,<scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> 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 ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Note that the location and scale parameters are optional.

LET A = RIGPPF(0.95,2,1)
LET A = RIGPPF(P1,2,1)
PLOT RIGPPF(P,2,1.5) FOR P = 0 0.01 0.99

None

None

RIGCDF	= Compute the reciprocal inverse Gaussian cumulative distribution function.
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.

"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.

Distributional Modeling

1990/5: Original implementation
2003/12: Modified to treat as a shape parameter instead of a location parameter

 
X1LABEL Probability
Y1LABEL 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 RIGPPF(P,2,1) FOR P = 0.01  0.01  
TITLE GAMMA = 5, MU = 1
PLOT RIGPPF(P,5,1) FOR P = 0.01  0.01  
TITLE GAMMA = 2, MU = 2
PLOT RIGPPF(P,2,2) FOR P = 0.01  0.01  
TITLE GAMMA = 5, MU = 2
PLOT RIGPPF(P,5,2) FOR P = 0.01  0.01  
END OF MULTIPLOT
JUSTIFICATION CENTER
MOVE 50 97
CASE ASIS
TEXT Reciprocal Inverse Gaussian Percent Point