PROGRAM alternative_hill_plot;

(* PROJECT          : Alternative Hill Plot   
   FILE-SPEC.       : althill.xpl   
   AUTHOR           : Arthur Boeshans, Carsten Wehn   
   CREATION DATE    : May-18-1998   
   LAST UPDATE      : May-18-1998   
   RELATED DOCUMENTS: Resnick, S.I. (1997). Heavy tail modeling and
                      telegraphic data. 
                      The Annals of Statistics 25, 1805-1869.   
   VERSION          : 0.99   
   FUNCTIONAL DESCR.: outputs alternative hill plot of active
                      univariate data set   
   SPECIAL FEATURES : none   
   INPUT            : Xtremes Univariate Data as active data set
   OUTPUT           : Alternative Hill Plot*)

VAR x,hillvector,theta : Vector of Real;

FUNCTION Hill (x:Realvector):Realvector;
VAR n: Integer;
BEGIN
  x:=Log(Rev(Sort(x[x>0])));
  n:=Size(x);
  Return (((Cumsum(x)) [1..(n-1)])/(1..(n-1)))-x [2..n];
END;

BEGIN
  x:=Columndata(1);
  hillvector:=1/Hill(x);
  theta:=Log(1..Size(hillvector))/Log(Size(hillvector));
  Plot(theta,hillvector,'Alternative Hill Plot','');  
END.