
STCDFName:
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 skewt reduces to a t distribution. As goes to infinity, the skewt tends to the foldedt distribution. The cumulative distribution is computed by numerically integrating the skewt probability density function. The standard skewt distribution can be generalized with location and scale parameters.
<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 skewt cdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = STCDF(A1,DF,LAMBDA) LET X2 = STCDF(X1,NU,0.5)
"LogSkewNormal and LogSkewt Distributions as Models for Familiy Income Data", Azzalini and Dal Cappello, unpublished paper downloaded from Azzallini web site.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 SKEWT (NU=3): LAMBDA = 0 PLOT STCDF(X,3,0) FOR X = 5 0.1 5 TITLE SKEWT (NU=3): LAMBDA = 1 PLOT STCDF(X,3,1) FOR X = 5 0.1 5 TITLE SKEWT (NU=3): LAMBDA = 5 PLOT STCDF(X,3,5) FOR X = 5 0.1 5 TITLE SKEWT (NU=3): LAMBDA = 10 PLOT STCDF(X,3,10) FOR X = 5 0.1 5 END OF MULTIPLOT
Date created: 2/3/2004 