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: ppsj2ind Description: computes the Sibson Jones index which considers the deviations from the normal density for bivariate 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 = ppsj2ind(x) Input: x n x 2 matrix containing the bivariate projected data Output: ind scalar, the corresponding Sibson Jones index for bivariate data

Example:
```; loads the library pp
library("pp")
; initialize random generator
randomize(0)
; generate a dataset with mean(x)=0 and cov(x)=I_2
x = normal(100,2)
; compute the index by means of Scott's rule
ppsj2ind(x)

```
Result:
```Contents of ind
[1,]  0.08592
```
Example:
```proc()= plotindex2(x, n)
p    = cols(x)
pv   = orthonormal(normal(p,2))
xp   = x*pv
imax = ppsj2ind(xp)
disp = createdisplay(1,2)
show(disp,1,2,xp)
; search now for a better projection
i = 0
while(i<n)
i   = i+1
pv  = orthonormal(normal(p,2))
xp  = x*pv
ind = ppsj2ind(xp)
show(disp,1,1,xp)
if(ind>imax)
imax = ind
show(disp,1,2,xp)
endif
endo
endp
library("plot")
library("math")
library("pp")
; sphere the data
x = transform(x, grc.prep.sphere)
randomize(0)
; choose number of projections
n = 100
plotindex2(x,n)

```
Result:
```We see two plots of projections of the data. In the left
display the actual projection is shown and in the right
display the best projection, which has been found so far
(the one with the highest index value) is shown.
```

Author: S. Klinke, L. Richter, 20011204
(C) MD*TECH Method and Data Technologies, 05.02.2006