 Dataplot Vol 2 Vol 1

# SNCDF

Name:
SNCDF (LET)
Type:
Library Function
Purpose:
Compute the skew-normal cumulative distribution function.
Description:
The skew-normal distribution has the following probability density function: For = 0, the skew-normal reduces to a normal distribution. As goes to , the skew-normal tends to the half-normal distribution.

The cumulative distribution function is computed by numerically integrating the skew-normal density function.

The standard skew-normal distribution can be generalized with location and scale parameters.

Syntax:
LET <y> = SNCDF(<x>,<lambda>,<loc>, <scale>)
<SUBSET/EXCEPT/FOR qualification>
where <x> is a variable or a parameter;
<lambda> is a number of parameter that specifies the value of the shape parameter;
<loc> is an optional number or parameter that specifies the value of the location parameter;
<scale> is an optional positive 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 skew-normal cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET A = SNCDF(3,1)
LET A = SNCDF(A1,LAMBDA)
LET X2 = SNCDF(X1,0.5)
Note:
Dataplot uses the DQAGI subroutine of Piessens and De Doncker from the Quadpack library of integration routines.
Default:
None
Synonyms:
None
Related Commands:
 SNPDF = Compute the skew-normal probability density function. SNPPF = Compute the skew-normal percent point function. NORPDF = Compute the normal density function. CHIPDF = Compute the chi probability density function. CHSPDF = Compute the chi-square probability density function. WEIPDF = Compute the Weibull probability density function.
Reference:
"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.

Applications:
Distributional Analysis, Bayesian Analysis
Implementation Date:
1/2004
Program:
```
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
TITLE SKEW-NORMAL: LAMBDA = 0
PLOT SNCDF(X,0) FOR X = -5 0.1 5
TITLE SKEW-NORMAL: LAMBDA = 1
PLOT SNCDF(X,1) FOR X = -5 0.1 5
TITLE SKEW-NORMAL: LAMBDA = 5
PLOT SNCDF(X,5) FOR X = -5 0.1 5
TITLE SKEW-NORMAL: LAMBDA = 10
PLOT SNCDF(X,10) FOR X = -5 0.1 5
END OF MULTIPLOT
``` Date created: 2/3/2004
Last updated: 2/3/2004