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Dataplot Vol 2 Vol 1

LSNCDF

Name:
    LSNCDF (LET)
Type:
    Library Function
Purpose:
    Compute the log-skew-normal cumulative distribution function.
Description:
    The log-skew-normal distribution can be defined in terms of the skew-normal distribution as follows:

      f(x,lambda,sd)=(1/(sd*x))*phi(LOG(x)/sd;lambda) 0 < x, sd < infinity; -infinity < lambda < infinity

    with lambda denoting the skewness parameter, sd denoting the standard deviation of the corresponding normal distribution, and phi(x;lambda denoting the probability density of the skew normal distribution.

    This is analogous to how the lognormal distribution is defined in terms of the normal distribution. If lamba = 0, the log-skew-normal distribution reduces to the lognormal distributiion.

    The log-skew-normal cumulative distribution is computed by numerically integrating the probability density function.

    The standard log-skew-normal distribution can be generalized with location and scale parameters in the usual way.

Syntax:
    LET <y> = LSNCDF(<x>,<lambda>,<sd>,<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 skewness shape parameter;
                <sd> is a number of parameter that specifies the value of the sd shape parameter;
                <loc> is a number of parameter that specifies the value of the location parameter;
                <scale> is a number of parameter that specifies the value of the scale parameter;
                <y> is a variable or a parameter (depending on what <x> is) where the computed log-skew-normal 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 = LSNCDF(3,1,1)
    LET A = LSNCDF(A1,LAMBDA,SD)
    LET X2 = LSNCDF(X1,0.5,1.5)
Default:
    None
Synonyms:
    None
Related Commands:
    LSNPDF = Compute the log-skew-normal probability density function.
    LSNPPF = Compute the log-skew-normal percent point function.
    SNPDF = Compute the skew-normal probability density function.
    NORPDF = Compute the normal density function.
    LGNPDF = Compute the lognormal 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:
    "Log-Skew-Normal and Log-Skew-t Distributions as Models for Family Income Data", Azzalini, Dal Cappello, and Kotz, Journal of Income Distribution, Vol. 11, No. 3-4, 2003, pp. 12-20.

    "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 Modeling
Implementation Date:
    3/2004
Program: 
     
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
X1LABEL DISPLACEMENT 12
Y1LABEL DISPLACEMENT 12
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
TITLE LOG-SKEW-NORMAL: LAMBDA = 0
PLOT LSNCDF(X,0) FOR X = 0.01  0.01  5
TITLE LOG-SKEW-NORMAL: LAMBDA = 1
PLOT LSNCDF(X,1) FOR X = 0.01  0.01  5
TITLE LOG-SKEW-NORMAL: LAMBDA = 5
PLOT LSNCDF(X,5) FOR X = 0.01  0.01  5
TITLE LOG-SKEW-NORMAL: LAMBDA = 10
PLOT LSNCDF(X,10) FOR X = 0.01  0.01  5
END OF MULTIPLOT
    plot generated by sample program

Date created: 7/7/2004
Last updated: 7/7/2004
Please email comments on this WWW page to alan.heckert@nist.gov.