Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Quantlet: ppsj1ind Description: computes the Sibson Jones index which considers the deviations from the normal density for univariate data.

Reference(s):
Sibson, R. and Jones, M. C. (1987). What Is Projection Pursuit? Journal of the Royal Statistical Society A(1987): 150. Part 1, pp. 1-36

 Usage: ind = ppsj1ind(px) Input: px n x 1 matrix containing the projected data Output: ind scalar, the corresponding Sibson Jones index

Example:
```; loads the library pp
library("pp")
; initialize random generator
randomize(0)
; generate a dataset with mean(x)=0 and var(x)=1
x = normal(100)
; compute the index with Scott's rule
ppsj1ind(x)

```
Result:
```Contents of ind
[1,]  0.0038037
```
Example:
```proc() = plotindex1(x)
n   = 50
phi = grid(0, 2*pi/n, n)
ind = NaN*matrix(n)
i   = 0
while(i<n)
i      = i+1
xp     = x * #(cos(phi[i]), sin(phi[i]))
ind[i] = ppsj1ind(xp)
line(phi~ind)
endo
endp
; load the library pp and plot
library("pp")
library("plot")
; select the fourth and sixth column and
; sphere the data
x = transform(x[,4|6], grc.prep.sphere)
; generate the index function for 1D projection
plotindex1(x)

```
Result:
```We see the plot of the index function in
dependence of the projection vector. The
projection vector is parametrized by the
angle phi. Since the projection vector v
and -v generate the same projection, we
see the index function doubled.
Note that the maxima at phi=1,76 and phi=2,8
represent the "most" interesting projections.
```

Author: S. Klinke, L. Richter, 20011203
(C) MD*TECH Method and Data Technologies, 05.02.2006