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LSTPDFName:
with STPDF denoting the skew-t distribution (enter HELP STPDF for details) and , , and sd denoting the shape parameters. For = 0, the log-skew-t reduces to a log-t distribution. The standard log-skew-t distribution can be generalized with location and scale parameters in the usual way.
<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; <sd> is a number or parameter that specifies the value of the standard deviation parameter; <loc> is a number or parameter that specifies the value of the location parameter; <scale> is a 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 log-skew-t pdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Note that the location and scale parameters are optional.
LET A = LSTPDF(A1,DF,LAMBDA,2) PLOT LSTPDF(X,NU,LAMBDA,SD) FOR X = 0.01 0.01 10
LET LAMBDA = <value> LET SD = <value> LET Y = LOG SKEW T RANDOM NUMBERS FOR I = 1 1 N LOG SKEW T PROBABILITY PLOT Y LOG SKEW T KOLMOGOROV SMIRNOV GOODNESS OF FIT Y LOG SKEW T CHI-SQUARE GOODNESS OF FIT Y
"Log-Skew-Normal and Log-Skew-t Distributions as Models for Family Income Data", Azzalini, Dal Cappello, and Kotz, Journal of Income Distribution, Vol. 11, No. 3-4, 2003, pp. 12-20.
Y1LABEL Probability X1LABEL X LABEL CASE ASIS X1LABEL DISPLACEMENT 12 Y1LABEL DISPLACEMENT 12 MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 100 LET SD = 1 TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 0 PLOT LSTPDF(X,3,0,SD) FOR X = 0.01 0.01 5 TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 1 PLOT LSTPDF(X,3,1,SD) FOR X = 0.01 0.01 5 TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 5 PLOT LSTPDF(X,3,5,SD) FOR X = 0.01 0.01 5 TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 10 PLOT LSTPDF(X,3,10,SD) FOR X = 0.01 0.01 5 END OF MULTIPLOT
Date created: 7/7/2004 |