/* Example 3.4.3-----Transformations to Achieve Normality*/
/* p=1, n=50, alpha=5% */
filename sriv1 'ch3p11.ext';
goptions  hsize=8cm vsize=6cm
device=pslepsf
gaccess=sasgaedt
gsfname=sriv1
gsfmode=replace;
/*gsflen=80;*/
libname sriv'/u/mengd/sasuser/ssm';
proc iml;
x={1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 1.5
   1.6 1.4 1.1 1.2 1.5 1.3 1.4 1.7 1.5 1.7 1.5
   1.0 1.7 1.9 1.6 1.6 1.5 1.4 1.6 1.6 1.5 1.5
   1.4 1.5 1.2 1.3 1.4 1.3 1.5 1.3 1.3 1.3 1.6
   1.9 1.4 1.6 1.4 1.5 1.4};
g1=exp(1/50*log(det(diag(x`))));
create sriv.maxLamda var{lamda lla};
do lamda=0.1 to 1 by 0.01;
y=(exp(lamda*log(x`))-1)/(lamda*exp((lamda-1)*log(g1)));
Yb=J(50,1,1)*J(1,50,1/50)*Y;
sLamdaSq=(Y-Yb)`*(Y-Yb)/(50-1);
integ=int(-(50-1)/2*log(sLamdaSq));
lLa=-(50-1)/2*log(sLamdaSq)-integ;
append;
end;
/* After having checked maximum point
   of lamda (0.85) then run the following */
y0=(exp(0.85*log(x`))-1)/(0.85*exp((0.85-1)*log(g1)));
create sriv.y0 var{y0 x};
append;
quit;
symbol1 I=spline  ;
proc gplot data=sriv.maxLamda;
plot lLa*lamda=1 /frame hminor=0  vminor=0 vaxis=0.4 to 0.8 by 0.1
     haxis=0.1 to 1 by 0.3 ;
run;
quit;
goptions hsize=0cm vsize=0cm goutmode=replace;
proc univariate data=sriv.y0  plot;
run;







                        
       0.95+                                           *   *  +
           |                                            ++++++
           |                                     **+**++
       0.65+                                *****++
           |                         *******+
           |                  *******++
       0.35+            ******+++
           |         **+++++
           |    +++*++
       0.05++++*
            +----+----+----+----+----+----+----+----+----+----+
                -2        -1         0        +1        +2