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Dataplot Vol 2 Vol 1

SDEPPF

Name:
    SDEPPF (LET)
Type:
    Library Function
Purpose:
    Compute the skew double exponential percent point function.
Description:
    The skew double exponential distribution has the following probability density function:

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

    To compute the percent point function, Dataplot computes the cumulative distribution function for X = 0. If this value is PCUT and p is the input probability value, then

      G(p,lambda) = LOG[2*p*(1-lambda)]/(1+lambda)] p <= PCUT

    If p is greater than PCUT, then Dataplot computes the percent point function by numerically inverting the cumulative distribution function.

    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 for the probability density function.

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

Syntax:
    LET <y> = SDEPPF(<p>,<lambda>,<loc>,<scale>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a variable, a number or a parameter in the interval (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 double exponential ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = SDEPPF(0.95,1)
    LET X = SDEPPF(P1,LAMBDA)
    PLOT SDEPPF(P,LAMBDA) FOR P = 0.01 0.01 0.99
Default:
    None
Synonyms:
    None
Related Commands:
    SDECDF = Compute the skew double exponential cumulative distribution function.
    SDEPDF = Compute the skew double exponential probability density function.
    ADEPDF = Compute the asymmetric double exponential probability density function.
    DEXPDF = Compute the double exponential probability density function.
    EXPPDF = Compute the exponential probability density function.
    SNPDF = Compute the skew normal probability density function.
    STPDF = 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: 
     
X1LABEL Probability
Y1LABEL X
LABEL CASE ASIS
TITLE CASE ASIS
CASE ASIS
X1LABEL DISPLACEMENT 12
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
TITLE Lambda = 0
PLOT SDEPPF(P,0) FOR P = 0.01 0.01 0.99
TITLE Lambda = 1
PLOT SDEPPF(P,1) FOR P = 0.01 0.01 0.99
TITLE Lambda = 5
PLOT SDEPPF(P,5) FOR P = 0.01 0.01 0.99
TITLE Lambda = 10
PLOT SDEPPF(P,10) FOR P = 0.01 0.01 0.99
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION 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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