STPDF
Name:
Type:
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:
Synonyms:
Related Commands:
STCDF
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= Compute the skew-t cumulative distribution function.
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STPPF
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= Compute the skew-t percent point function.
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SNPDF
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= Compute the skew-normal probability density function.
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TPDF
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= Compute the t probability density function.
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FTPDF
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= Compute the folded t probability density function.
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NORPDF
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= Compute the normal density function.
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CHSPDF
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= Compute the chi-square probability density function.
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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:
Implementation Date:
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
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[email protected].
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