Dataplot Vol 2 Vol 1

Name:
Type:
Library Function
Purpose:
Compute the asymmetric double exponential probability density function.
Description:
The asymmetric double exponential distribution has the following probability density function:

with denoting the shape parameter.

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

in the above formula.

If = 1 and the scale parameter = , the asymmetric double exponential distribution reduces to the symmetric double exponential distribution.

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

Syntax:
<SUBSET/EXCEPT/FOR qualification>
where <x> is a variable or a parameter;
<k> is a positive 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 asymmetric double exponential pdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
PLOT ADEPDF(X,K) FOR X = -5 0.01 5
Note:
Kotz, Kozubowski, and Podgorski define an alternate parameterization based on the parameter . These parameterizations are related by:

The parameter can be any real number. A value of = 0 reduces to the symmetric double exponential (i.e., = 1).

By default, Dataplot uses the parameterization. To use the parameterization, enter the command

SET ASYMMETRIC DOUBLE EXPONENTIAL DEFINITION MU

To reset the parameterization, enter the command

SET ASYMMETRIC DOUBLE EXPONENTIAL DEFINITION K
Note:
To generate asymmetric double exponential random numbers, enter the commands

LET K = <value> LET Y = ASYMMETRIC DOUBLE EXPONENTIAL RANDOM NUMBERS ...
FOR I = 1 1 N

To generate an asymmetric double exponential probability plot or an asymmetric double exponential Kolmogorov-Smirnov or chi-square goodness of fit test, enter the following commands

LET K = <value> ASYMMETRIC DOUBLE EXPONENTIAL PROBABILITY PLOT Y
ASYMMETRIC DOUBLE EXPONENTIAL KOLMOGOROV SMIRNOV ...
GOODNESS OF FIT Y
ASYMMETRIC DOUBLE EXPONENTIAL CHI-SQUARE GOODNESS OF FIT Y

To generate a PPCC or Kolmogorov-Smirnov plot, enter the following commands

LET K1 = <value>
LET K2 = <value>
ASYMMETRIC DOUBLE EXPONENTIAL PPCC PLOT Y
ASYMMETRIC DOUBLE EXPONENTIAL KS PLOT Y

The default values for K1 and K2 are 0.2 and 10.

If you have requested the parameterization, then you you need to enter the command

LET MU = <value>

in place of

LET K = <value>
and

LET MU1 = <value>
LET MU2 = <value>

in place of

LET K1 = <value>
LET K2 = <value>
Default:
None
Synonyms:
None
Related Commands:
 ADECDF = Compute the asymmetric double exponential cumulative distribution function. ADEPPF = Compute the asymmetric double exponential percent point function. SDEPDF = Compute the skew 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, pp. 133-174.

"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
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 95
MULTIPLOT SCALE FACTOR 2
TITLE Kappa = 0.5
PLOT ADEPDF(X,0.5) FOR X = -5 0.1 5
TITLE Kappa = 1
PLOT ADEPDF(X,1) FOR X = -5 0.1 5
TITLE Kappa = 2
PLOT ADEPDF(X,2) FOR X = -5 0.1 5
TITLE Kappa = 5
PLOT ADEPDF(X,5) FOR X = -5 0.1 5
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATIONC CENTER
TEXT Asymmetric Double Exponential Distribution
```

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