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LSNPDFName:
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with
This is analogous to how the lognormal distribution is defined
in terms of the normal distribution. If
The standard log-skew-normal 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; <lambda> is a number of parameter that specifies the value of the skewness shape parameter; <sd> is a number of parameter that specifies the value of the sd shape parameter; <loc> is a number of parameter that specifies the value of the location parameter; <scale> is a number of 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-normal pdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Note that the location and scale parameters are optional.
LET A = LSNPDF(A1,LAMBDA,SD) LET X2 = LSNPDF(X1,0.5,1.5)
LET SD = <value> LET Y = LOG SKEW NORMAL RANDOM NUMBERS FOR I = 1 1 N LOG SKEW NORMAL PROBABILITY PLOT Y LOG SKEW NORMAL KOLMOGOROV SMIRNOV GOODNESS OF FIT Y LOG SKEW NORMAL CHI-SQUARE GOODNESS OF FIT Y The following commands can be used to estimate the shape parameters for the log-skew-normal distribution:
LET LAMBDA2 = <value> LET SD1 = <value> LET SD2 = <value> LOG SKEW NORMAL PPCC PLOT Y LOG SKEW NORMAL KS PLOT Y
"A Class of Distributions Which Includes the Normal Ones", Azzalini, Scandinavian Journal of Statistics, 12, 171-178. "Continuous Univariate Distributions: Volume I", Second Edition, Johnson, Kotz, and Balakrishnan, Wiley, 1994, p. 454.
Y1LABEL Probability X1LABEL X LABEL CASE ASIS X1LABEL DISPLACEMENT 12 Y1LABEL DISPLACEMENT 12 MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 100 TITLE LOG-SKEW-NORMAL: LAMBDA = 0 PLOT LSNPDF(X,0) FOR X = 0.01 0.01 5 TITLE LOG-SKEW-NORMAL: LAMBDA = 1 PLOT LSNPDF(X,1) FOR X = 0.01 0.01 5 TITLE LOG-SKEW-NORMAL: LAMBDA = 5 PLOT LSNPDF(X,5) FOR X = 0.01 0.01 5 TITLE LOG-SKEW-NORMAL: LAMBDA = 10 PLOT LSNPDF(X,10) FOR X = 0.01 0.01 5 END OF MULTIPLOT ![]()
Date created: 7/7/2004 |