(* Statistics/Normal distribution *)

block

  (* Generates normally distributed random numbers with mean 0 and standard deviation 1 *)
  unit random_normal: function: real;
  const
    pi = 3.14159265358979;
  begin
    result := cos(2.0 * pi * random) * sqrt(-2.0 * ln(random))
  end random_normal;

  unit normal_stats: procedure (sample_size: integer);
  var
    r: arrayof real,
    sum, mean, diff, scale, sd: real,
    h: arrayof integer,
    h_sum, adj, i, j: integer;
  begin
    if sample_size < 1 then return fi;

    array r dim (1 : sample_size);
    array h dim (-1 : 10); (* all zero by default *)
    sum := 0.0;
    h_sum := 0;

    (* Generate 'sample_size' normally distributed random numbers with mean 0.5
      and standard deviation 0.25.
      Calculate their sum and in which box they will fall when drawing
      the histogram. *)
    for i := 1 to sample_size
    do
      r(i) := .5 + random_normal / 4.0;
      sum := sum + r(i);
      if r(i) < 0.0
      then h(-1) := h(-1) + 1
      else
        if r(i) >= 1.0
        then h(10) := h(10) + 1
        else h(entier(r(i) * 10)) := h(entier(r(i) * 10)) + 1
        fi
      fi
    od;

    for i := -1 to 10 do h_sum := h_sum + h(i) od;
    (* Adjust one of the h() values if necessary to ensure h_sum = sample_size *)
    adj := sample_size - h_sum;
    if adj =/= 0
    then
      for i := -1 to 10
      do
        h(i) := h(i) + adj;
        if h(i) >= 0 then exit fi;
        h(i) := h(i) - adj
      od
    fi;
    mean := sum / sample_size;

    (* Now calculate their standard deviation *)
    sum := 0.0;
    for i := 1 to sample_size
    do
      diff := r(i) - mean;
      sum := sum + diff * diff
    od;
    sd := sqrt(sum / sample_size);

    (* Draw a histogram of the data with interval 0.1
      If sample size > 300 then normalize histogram to 300 *)
    scale := 1.0;
    if sample_size > 300 then scale := 300.0 / sample_size fi;
    writeln("Sample size ", sample_size);
    writeln("  Mean ", mean: 8: 6, "  SD ", sd: 8: 6);
    for i := -1 to 10
    do
      if i = -1 then write("< 0.00 : ")
      else
        if i = 10
        then write(">=1.00 : ")
        else write("  ", i / 10.0 : 4: 2, " : ")
        fi
      fi;
      write(h(i): 5, " ");
      for j := 1 to entier(h(i) * scale + .5) do write("*") od;
      writeln
    od;
  end normal_stats;

begin
  call normal_stats(100);
  writeln;
  call normal_stats(1000);
  writeln;
  call normal_stats(10000);
  writeln;
end;