Dataplot Vol 2 Vol 1

# LSTPPF

Name:
LSTPPF (LET)
Type:
Library Function
Purpose:
Compute the log-skew-t percent point function.
Description:
The log-skew-t distribution has the following probability density function:

with STPDF denoting the skew-t distribution (enter HELP STPDF for details) and , , and sd denoting the shape parameters.

The percent point function is computed by numerically inverting the cumulative distribution function using a bisection mehtod. The cumulative distribution function is computed by numerically integrating the log-skew-t probability density function.

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.

Syntax:
LET <y> = LSTPPF(<p>,<nu>,<lambda>,<sd>,<loc>,<scale>)
<SUBSET/EXCEPT/FOR qualification>
where <p> is a variable or a parameter in the range (0,1);
<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 ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

Note that the location and scale parameters are optional.

Examples:
LET A = LSTPPF(0.95,5,1,2)
LET A = LSTPPF(P,DF,LAMBDA,2)
PLOT LSTPPF(P,NU,LAMBDA,SD) FOR P = 0.01 0.01 0.99
Default:
None
Synonyms:
None
Related Commands:
= Compute the log-skew-t probability density function.  LSTCDF = Compute the log-skew-t cumulative distribution function. LSTPDF STPDF = Compute the skew-t probability density function. SNPDF = Compute the skew-normal probability density function. TPDF = Compute the t probability density function. FTPDF = Compute the folded t probability density function. NORPDF = Compute the normal density function. CHSPDF = Compute the chi-square probability density function.
Reference:
"A Class of Distributions Which Includes the Normal Ones", Azzalini, Scandinavian Journal of Statistics, 12, 171-178.

"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.

Applications:
Distributional Modeling
Implementation Date:
1/2004
Program:
```
X1LABEL Probability
Y1LABEL 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 LSTPPF(P,3,0,SD) FOR P = 0.01 0.01 0.95
TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 1
PLOT LSTPPF(P,3,1,SD) FOR P = 0.01 0.01 0.95
TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 5
PLOT LSTPPF(P,3,5,SD) FOR P = 0.01 0.01 0.95
TITLE LOG-SKEW-T (NU=3, SD=1): LAMBDA = 10
PLOT LSTPPF(P,3,10,SD) FOR P = 0.01 0.01 0.95
END OF MULTIPLOT
```

Date created: 7/7/2004
Last updated: 7/7/2004