/*-------------------------------------------*/
/*  Some basic statistics                    */
/*-------------------------------------------*/
/*  (C) 2004 Zdravko Markov                  */
/*-------------------------------------------*/
/*  Procedures:                              */
/*    mean(+List, -Mean)                     */
/*    stdev(+List, -Deviation)               */
/*    variance(+List, -Variance)             */
/*    p(+Value, +Mean, +Deviation, -Density) */
/*    p(+Value, +List, -Density)             */
/*-------------------------------------------*/

mean(L,M) :-
   length(L,N),
   sum(L,S),
   M is S/N.

sum([],0) :- !.
sum([X|T],S) :-
   sum(T,S1),
   S is S1+X.

stdev(L,D) :-
   variance(L,V),
   D is sqrt(V).

variance([_],0) :- !.
variance(L,V) :-
   length(L,N),
   mean(L,M),
   sumsq(L,M,S),
   V is S/(N-1).

sumsq([],_,0) :- !.
sumsq([X|T],M,S) :-
   sumsq(T,M,S1),
   S is S1+(X-M)*(X-M).

p(X,M,D,P) :- 
   P is exp(-(X-M)*(X-M)/(2*D*D))/(D*sqrt(2*pi)).

p(X,L,P) :- 
   mean(L,M),
   stdev(L,D),
   p(X,M,D,P).