program TMLE;

(*
   PROJECT          : StatPascal demonstration program.
   FILE-SPEC.       : tmle.sp
   AUTHOR           : R.-D. Reiss, M. Thomas
   CREATION DATE    : Apr-19-2000
   LAST UPDATE      : Dec-6-2000
   VERSION          : 1.0
   RELATED FILES    : Requires unit maximize.sp
   FUNCTIONAL DESCR.: MLE for Student distribution
   SPECIAL FEATURES : requires Xtremes Version 3.0 
*)

uses maximize;

var x: realvector;

function f (theta: realvector): real;
    
    function tden (x: real): real;
	begin
	    return tdensity (theta [1], x / theta [2]) / theta [2]
	end;

    begin
	return sum (log (tden (x)))
    end;

function c (theta: realvector): boolean;
    begin
	return (theta [1] > 0.0) and (theta [2] > 0.0)
    end;

var alpha, mu, sigma: real;
    res: integer;
    d1: realvector;

begin
    x := columndata (1);
    HillGP1 (x, size (x) div 10, alpha, mu, sigma, res);
    sigma := (sort (x)) [8 * size (x) div 10] / tqf (alpha, 0.8);
    writeln ('Pre-Est: alpha = ', alpha, ', sigma = ', sigma);    
    d1 := searchmax (f, combine (alpha, sigma), c, 2);
    writeln ('MLE: alpha = ', d1 [1], ', sigma = ', d1 [2])
end.