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Dataplot Vol 2 Vol 1

SNPDF

Name:
    SNPDF (LET)
Type:
    Library Function
Purpose:
    Compute the skew-normal probability density function.
Description:
    The skew-normal distribution has the following probability density function:

      f(x,lambda)=2*NORCDF(lambda*x)*NORPDF(x) -infinity < x, lambda < infinity

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

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

Syntax:
    LET <y> = SNPDF(<x>,<lambda>,<loc>, <scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable or a parameter;
                <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 pdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = SNPDF(3,1)
    LET A = SNPDF(A1,LAMBDA)
    LET X2 = SNPDF(X1,0.5)
Default:
    None
Synonyms:
    None
Related Commands:
    SNCDF = Compute the skew-normal cumulative distribution function.
    SNPPF = Compute the skew-normal percent point 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.
Reference:
    "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.

Applications:
    Distributional Analysis, Bayesian Analysis
Implementation Date:
    1/2004
Program: 
     
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
TITLE SKEW-NORMAL: LAMBDA = 0
PLOT SNPDF(X,0) FOR X = -5 0.1 5
TITLE SKEW-NORMAL: LAMBDA = 1
PLOT SNPDF(X,1) FOR X = -5 0.1 5
TITLE SKEW-NORMAL: LAMBDA = 5
PLOT SNPDF(X,5) FOR X = -5 0.1 5
TITLE SKEW-NORMAL: LAMBDA = 10
PLOT SNPDF(X,10) FOR X = -5 0.1 5
END OF MULTIPLOT

    plot generated by sample program

Date created: 2/3/2004
Last updated: 2/3/2004
Please email comments on this WWW page to alan.heckert@nist.gov.