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Dataplot Vol 2 Vol 1

SDECDF

Name:
    SDECDF (LET)
Type:
    Library Function
Purpose:
    Compute the skew double exponential cumulative distribution function.
Description:
    The skew double exponential distribution has the following cumulative distribution function:

      F(x,lambda)=0.5*EXP((1+lambda)*x)/(1+LAMBDA) - infinity < x <= 0 =1 + EXP(-x) - 0.5/(EXP((1+lambda)*x)*(-1-lambda)) 0 < x < infinity lambda >= 0

    For lambda = 0, the skew double exponential reduces to the double exponential distribution. As lambda goes to infinity, the skew double exponential tends to the exponential distribution.

    The standard skew double exponential distribution can be generalized with a location parameter, mu, and a scale parameter sigma. Simply replace x with

      (x-mu)/sigma

    in the above formula.

    The skew double exponential distribution is also known as the skew Laplace distribution.

Syntax:
    LET <y> = SDECDF(<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 double exponential cdf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET Y = SDECDF(3,1)
    LET Y = SDECDF(X1,LAMBDA)
    PLOT SDECDF(X,LAMBDA) FOR X = -5 0.1 5
Default:
    None
Synonyms:
    None
Related Commands:
    SDEPDF = Compute the skew double exponential probability density function.
    SDEPPF = Compute the skew double exponential percent point function.
    ADEPDF = Compute the asymmetric double exponential probability density function.
    DEXCDF = Compute the double exponential probability density function.
    EXPCDF = Compute the exponential probability density function.
    SNCDF = Compute the skew normal probability density function.
    STCDF = Compute the skew t probability density function.
Reference:
    "The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance", Birkhauser, 2001, p. 136.

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

Applications:
    Distributional Modeling
Implementation Date:
    6/2004
Program: 
     
Y1LABEL Probability
X1LABEL X
LABEL CASE ASIS
TITLE CASE ASIS
CASE ASIS
Y1LABEL DISPLACEMENT 12
X1LABEL DISPLACEMENT 12
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
TITLE Lambda = 0
PLOT SDECDF(X,0) FOR X = -5 0.1 5
TITLE Lambda = 1
PLOT SDECDF(X,1) FOR X = -5 0.1 5
TITLE Lambda = 5
PLOT SDECDF(X,5) FOR X = -5 0.1 5
TITLE Lambda = 10
PLOT SDECDF(X,10) FOR X = -5 0.1 5
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATIONC CENTER
TEXT Skew Double Exponential Distribution
    plot generated by sample program

Date created: 7/7/2004
Last updated: 7/7/2004
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