IGAPDF

IGAPDF (LET)

Library Function

Compute the standard form of the inverted gamma probability density function.

The standard form of the generalized gamma distribution has the following probability density function:

where k and c are shape parameters and is the complete gamma function.

The inverted gamma is the special case where the second shape parameter, c, is equal to -1.

LET <y2> = IGAPDF(<y1>,<k>, <loc>,<scale>)             <SUBSET/EXCEPT/FOR qualification>
where <y1> is a positive number, parameter, or a variable;
            <y2> is a variable or a parameter (depending on what <y1> is) where the computed inverted gamma pdf value is saved;
            <k> is a positive number, parameter, or variable that specifies the first shape parameter;
            <loc> is a number, parameter, or variable that defines the location parameter;
            <scale> is a number, parameter, or variable that defines the scale parameter;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

LET A = IGAPDF(3,1.5)
LET Y = IGAPDF(X,1.5)
LET Y = IGAPDF(X,1.5,10,2)
PLOT IGAPDF(X,1.5,10,2) FOR X = 5 0.1 15

The general form of the generalized gamma distribution is:

The parameter a is a location parameter and the parameter b is a scale parameter. The inverted gamma distribution is the special case where c = -1. The IGAPDF function allows the location and scale parameters to optionally be specified.

To generate an inverted gamma probability plot, enter the following commands.
LET GAMMA = <value>
INVERTED GAMMA PROBABILITY PLOT


To generate an inverted gamma ppcc plot, enter the following commands.

LET GAMMA = <value>
INVERTED GAMMA PPCC PLOT

None

None

IGACDF	= Compute the inverted gamma cumulative distribution function.
IGAPPF	= Compute the inverted gamma percent point function.
GGDCDF	= Compute the generalized gamma cumulative distribution function.
GGDPDF	= Compute the generalized gamma probability density function.
GGDPPF	= Compute the generalized gamma percent point function.
GAMCDF	= Compute the gamma cumulative distribution function.
GAMPDF	= Compute the gamma probability density function.
GAMPPF	= Compute the gamma percent point function.
WEICDF	= Compute the Weibull cumulative distribution function.
WEIPDF	= Compute the Weibull probability density function.
WEIPPF	= Compute the Weibull percent point function.
EXPCDF	= Compute the exponential cumulative distribution function.
EXPPDF	= Compute the exponential probability density function.
EXPPPF	= Compute the exponential percent point function.
CHSCDF	= Compute the chi-square cumulative distribution function.
CHSPDF	= Compute the chi-square probability density function.
CHSPPF	= Compute the chi-square percent point function.

"Continuous Univariate Distributions", 2nd. ed., Johnson, Kotz, and Balakrishnan, John Wiley and Sons, 1994 (chapter 17).

"Statistical Distributions", 2nd. Edition, Evans, Hastings, and Peacock, Wiley and Sons, 1993 (chapter 18).

Reliability

1998/5

LET G = DATA 0.5 1 2 5
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
TITLE AUTOMATIC
LOOP FOR K = 1 1 4
LET G1 = G(K)
X1LABEL GAMMA = ^G1
PLOT IGAPDF(X,G1) FOR X = 0.1 0.1 10
END OF LOOP
END OF MULTIPLOT