 Dataplot Vol 2 Vol 1

# STPDF

Name:
STPDF (LET)
Type:
Library Function
Purpose:
Compute the skew-t probability density function.
Description:
The skew-t distribution has the following probability density function: with , , TCDF, and TPDF denoting the degrees of freedom parameter, the skewness parameter, the cumulative distribution function of the t distribution, and the probability density function of the t distribution, respectively.

For = 0, the skew-t reduces to a t distribution. As goes to infinity, the skew-t tends to the folded-t distribution.

The standard skew-t distribution can be generalized with location and scale parameters.

Syntax:
LET <y> = STPDF(<x>,<nu>,<lambda>)
<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;
<y> is a variable or a parameter (depending on what <x> is) where the computed skew-t pdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = STPDF(3,5,1)
LET A = STPDF(A1,DF,LAMBDA)
LET X2 = STPDF(X1,NU,0.5)
Default:
None
Synonyms:
None
Related Commands:
 STCDF = Compute the skew-t cumulative distribution function. STPPF = Compute the skew-t percent point 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"Log-Skew-Normal and Log-Skew-t Distributions as Models for Familiy Income Data", Azzalini and Dal Cappello, unpublished paper downloaded from Azzallini web site.

Applications:
Distributional Modeling
Implementation Date:
1/2004
Program:
```
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
TITLE SKEW-T (NU=3): LAMBDA = 0
PLOT STPDF(X,3,0) FOR X = -5 0.1 5
TITLE SKEW-T (NU=3): LAMBDA = 1
PLOT STPDF(X,3,1) FOR X = -5 0.1 5
TITLE SKEW-T (NU=3): LAMBDA = 5
PLOT STPDF(X,3,5) FOR X = -5 0.1 5
TITLE SKEW-T (NU=3): LAMBDA = 10
PLOT STPDF(X,3,10) FOR X = -5 0.1 5
END OF MULTIPLOT
``` Date created: 2/3/2004
Last updated: 2/3/2004