
LSNCDFName:
with denoting the skewness parameter, sd denoting the standard deviation of the corresponding normal distribution, and denoting the probability density of the skew normal distribution. This is analogous to how the lognormal distribution is defined in terms of the normal distribution. If = 0, the logskewnormal distribution reduces to the lognormal distributiion. The logskewnormal cumulative distribution is computed by numerically integrating the probability density function. The standard logskewnormal 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 logskewnormal cdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional. Note that the location and scale parameters are optional.
LET A = LSNCDF(A1,LAMBDA,SD) LET X2 = LSNCDF(X1,0.5,1.5)
"A Class of Distributions Which Includes the Normal Ones", Azzalini, Scandinavian Journal of Statistics, 12, 171178. "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 LOGSKEWNORMAL: LAMBDA = 0 PLOT LSNCDF(X,0) FOR X = 0.01 0.01 5 TITLE LOGSKEWNORMAL: LAMBDA = 1 PLOT LSNCDF(X,1) FOR X = 0.01 0.01 5 TITLE LOGSKEWNORMAL: LAMBDA = 5 PLOT LSNCDF(X,5) FOR X = 0.01 0.01 5 TITLE LOGSKEWNORMAL: LAMBDA = 10 PLOT LSNCDF(X,10) FOR X = 0.01 0.01 5 END OF MULTIPLOT
Date created: 7/7/2004 