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STPPFName:
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 skew-t percent point function is computed numerically (by inverting the skew-t cdf function with the bisection method). The standard skew-t distribution can be generalized with location and scale parameters.
<SUBSET/EXCEPT/FOR qualification> where <p> is a variable or a parameter in the range [0,1]; <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 <p> is) where the computed skew-t ppf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = STPPF(A1,DF,LAMBDA) LET X2 = STPPF(P1,NU,0.5)
"Log-Skew-Normal and Log-Skew-t Distributions as Models for Familiy Income Data", Azzalini and Dal Cappello, unpublished paper downloaded from Azzallini web site.
MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 100 TITLE SKEW-T (NU=3): LAMBDA = 0 PLOT STPPF(P,3,0) FOR P = 0.01 0.01 0.99 TITLE SKEW-T (NU=3): LAMBDA = 1 PLOT STPPF(P,3,1) FOR P = 0.01 0.01 0.99 TITLE SKEW-T (NU=3): LAMBDA = 5 PLOT STPPF(P,3,5) FOR P = 0.01 0.01 0.99 TITLE SKEW-T (NU=3): LAMBDA = 10 PLOT STPPF(P,3,10) FOR P = 0.01 0.01 0.99 END OF MULTIPLOT
Date created: 2/3/2004 |