Data update

Task/Statistics-Normal-distribution/Loglan82/statistics-normal-distribution.loglan82

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+(* 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;