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Dataplot Vol 2 Vol 1

LSTCDF

Name:
    LSTCDF (LET)
Type:
    Library Function
Purpose:
    Compute the log-skew-t cumulative distribution function.
Description:
    The log-skew-t distribution has the following probability density function:

      f(x,nu,lambda,sd)=(1/(sd*x))**STPDF(LOG(x)/sd,nu,lambda,sd) x, lambda, sd > 0; nu a positive integer

    with STPDF denoting the skew-t distribution (enter HELP STPDF for details) and lambda, nu, and sd denoting the shape parameters.

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

    For lambda = 0, the log-skew-t reduces to a log-t distribution.

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

Syntax:
    LET <y> = LSTCDF(<x>,<nu>,<lambda>,<sd>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable or a parameter;
                <nu> is a number of parameter that specifies the value of the degrees of freedom shape parameter;
                <lambda> is a number of parameter that specifies the value of the skewness shape parameter;
                <sd> is a number or parameter that specifies the value of the standard deviation parameter;
                <loc> is a number or parameter that specifies the value of the location parameter;
                <scale> is a 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 log-skew-t 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 = LSTCDF(3,5,1,2)
    LET A = LSTCDF(A1,DF,LAMBDA,2)
    PLOT LSTCDF(X,NU,LAMBDA,SD) FOR X = 0.01 0.01 10
Default:
    None
Synonyms:
    None
Related Commands:
    LSTPDF = Compute the log-skew-t probability density function.
    LSTPPF = Compute the log-skew-t percent point function.
    STPDF = Compute the skew-t probability density function.
    SNPDF = Compute the skew-normal probability density function.
    TPDF = Compute the t probability density function.
    FTPDF = Compute the folded t probability density function.
    NORPDF = Compute the normal density function.
    CHSPDF = Compute the chi-square probability density function.
Reference:
    "A Class of Distributions Which Includes the Normal Ones", Azzalini, Scandinavian Journal of Statistics, 12, 171-178.

    "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.

Applications:
    Distributional Modeling
Implementation Date:
    1/2004
Program: 
     
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
X1LABEL DISPLACEMENT 12
Y1LABEL DISPLACEMENT 12
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
LET SD = 1
TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 0
PLOT LSTCDF(X,3,0,SD) FOR X = 0.01  0.01  5
TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 1
PLOT LSTCDF(X,3,1,SD) FOR X = 0.01 0.01  5
TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 5
PLOT LSTCDF(X,3,5,SD) FOR X = 0.01  0.01  5
TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 10
PLOT LSTCDF(X,3,10,SD) 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.