SNPPF

SNPPF (LET)

Library Function

Compute the skew-normal percent point function.

The skew-normal distribution has the following probability density function:

For = 0, the skew-normal reduces to a normal distribution. As goes to , the skew-normal tends to the half-normal distribution.

The skew-normal percent point function is computed by numerically inverting the skew-normal cumulative distribution function (which in turn is computed by numerically integrating the skew-normal density function).

The standard skew-normal distribution can be generalized with location and scale parameters.

LET <y> = SNPPF(<p>,<lambda>,<loc>, <scale>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> is a variable or a parameter in the range (0,1);
            <lambda> is a number of parameter that specifies the value of the shape parameter;
            <loc> is an optional number or parameter that specifies the value of the location parameter;
            <scale> is an optional positive number or parameter that specifies the value of the scale parameter;
            <y> is a variable or a parameter (depending on what <x> is) where the computed skew-normal ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = SNPPF(0.95,1)
LET A = SNPPF(A1,LAMBDA)
LET X = SNPPF(P1,0.5)

None

None

SNCDF	= Compute the skew-normal cumulative distribution function.
SNPDF	= Compute the skew-normal probability density function.
NORPDF	= Compute the normal density function.
CHIPDF	= Compute the chi probability density function.
CHSPDF	= Compute the chi-square probability density function.
WEIPDF	= Compute the Weibull probability density function.

"A Class of Distributions Which Includes the Normal Ones", Azzalini, Scandinavian Journal of Statistics, 12, 171-178.

"Continuous Univariate Distributions: Volume I", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 454.

Distributional Analysis, Bayesian Analysis

1/2004

 
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
TITLE SKEW-NORMAL: LAMBDA = 0
PLOT SNPPF(P,0) FOR P = 0.01 0.01 0.99
TITLE SKEW-NORMAL: LAMBDA = 1
PLOT SNPPF(P,1) FOR P = 0.01 0.01 0.99
TITLE SKEW-NORMAL: LAMBDA = 5
PLOT SNPPF(P,5) FOR P = 0.01 0.01 0.99
TITLE SKEW-NORMAL: LAMBDA = 10
PLOT SNPPF(P,10) FOR P = 0.01 0.01 0.99
END OF MULTIPLOT