Initial data commit

Task/Statistics-Normal-distribution/Pascal/statistics-normal-distribution.pas

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+Program Example40;
+{$IFDEF FPC}
+  {$MOde objFPC}
+{$ENDIF}
+{ Program to demonstrate the randg function. }
+Uses Math;
+
+type
+  tTestData =  extended;//because of math.randg
+  ttstfunc = function  (mean, sd: tTestData): tTestData;
+  tExArray = Array of tTestData;
+  tSolution = record
+                SolExArr : tExArray;
+                SollowVal,
+                SolHighVal,
+                SolMean,
+                SolStdDiv : tTestData;
+                SolSmpCnt : LongInt;
+              end;
+
+function getSol(genFunc:ttstfunc;Mean,StdDiv: tTestData;smpCnt: LongInt): tSolution;
+var
+  GenValue,
+  sumValue,
+  sumsqrVal : extended;
+Begin
+  with result do
+  Begin
+    SolSmpCnt  := smpCnt;
+    SolMean    := 0;
+    SolStdDiv  := 0;
+    SolLowVal  := Mean+50* StdDiv;
+    SolHighVal := Mean-50* StdDiv;
+    setlength(SolExArr,smpCnt);
+    if smpCnt <= 0 then
+      EXIT;
+    sumValue   := 0;
+    sumsqrVal  := 0;
+    repeat
+      GenValue   := genFunc(Mean,StdDiv);
+      sumValue   := sumvalue+GenValue;
+      sumsqrVal  :=  sumsqrVal+sqr(GenValue);
+      IF GenValue < SollowVal then
+        SollowVal:= GenValue
+      else
+        IF GenValue > SolHighVal then
+           SolHighVal := GenValue;
+      dec(smpCnt);
+      SolExArr[smpCnt] := GenValue;
+    until smpCnt<= 0;
+    SolMean := sumValue/SolSmpCnt;
+    SolStdDiv := sqrt(sumsqrVal/SolSmpCnt-sqr(SolMean));
+  end;
+end;
+
+//http://wiki.freepascal.org/Generating_Random_Numbers#Normal_.28Gaussian.29_Distribution
+function rnorm (mean, sd: tTestData): tTestData;
+ {Calculates Gaussian random numbers according to the Box-Müller approach}
+  var
+   u1, u2: extended;
+ begin
+   u1 := random;
+   u2 := random;
+   rnorm := mean * abs(1 + sqrt(-2 * (ln(u1))) * cos(2 * pi * u2) * sd);
+  end;
+
+procedure Histo(const sol:TSolution;Colcnt,ColLen :LongInt);
+var
+  CntHisto : array of integer;
+  LoLmt,HiLmt,span : tTestData;
+  i, j,cnt,maxCnt: LongInt;
+  sCross : Ansistring;
+Begin
+  setlength(CntHisto,Colcnt);
+  with Sol do
+  Begin
+    span := solHighVal-solLowVal;
+    LoLmt := solLowVal;
+    writeln('Count: ',SolSmpCnt:10,' Mean ',SolMean:10:6,' StdDiv ',SolStdDIv:10:6);
+    writeln('span : ',span:10:5,' Low  ',solLowVal:10:6,'   high ',solHighVal:10:6);
+
+  end;
+  maxCnt := 0;
+  For j := 0 to Colcnt-1 do
+  Begin
+    HiLmt:= LoLmt+span/Colcnt;
+    cnt := 0;
+    with sol do
+      For i := 0 to High(SolExArr) do
+         IF (HiLmt > SolExArr[i]) AND  (SolExArr[i]>= LoLmt) then
+            inc(cnt);
+    CntHisto[j] := cnt;
+    IF maxCnt < cnt then
+      maxCnt := cnt;
+    LoLmt:=  HiLmt;
+  end;
+  inc(CntHisto[Colcnt]); // for HiLmt itself
+  writeln;
+  LoLmt := sol.solLowVal;
+  For i := 0 to Colcnt-1 do
+  Begin
+    Writeln(LoLmt:8:4,': ');
+    cnt:= Round(CntHisto[i]*ColLen/maxCnt);
+    setlength(sCross,cnt+3);
+    fillChar(sCross[1],3,' ');
+    fillChar(sCross[4],cnt,'#');
+    writeln(CntHisto[i]:10,sCross);
+    LoLmt := LoLmt+span/Colcnt;
+  end;
+  Writeln(sol.solHighVal:8:4,': ');
+end;
+
+const
+  cHistCnt = 11;
+  cColLen = 65;
+
+  cStdDiv = 0.25;
+  cMean   = 20*cStdDiv;
+var
+  mySol : tSolution;
+begin
+  Randomize;
+  // test of randg of unit math
+  Writeln('function randg');
+  mySol := getSol(@randg,cMean,cMean*cStdDiv,100000);
+  Histo(mySol,cHistCnt,cColLen);
+  writeln;
+  // test of rnorm from wiki
+  Writeln('function rnorm');
+  mySol := getSol(@rnorm,cMean,cStdDiv,1000000);
+  Histo(mySol,cHistCnt,cColLen);
+end.