LazStats: Show cumulative probabilities in DistribUnit

git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7639 8e941d3f-bd1b-0410-a28a-d453659cc2b4

applications/lazstats/source/LazStats.lpi

@@ -1429,6 +1429,11 @@
         <DebugInfoType Value="dsDwarf2"/>
       </Debugging>
       <LinkSmart Value="True"/>
+      <Options>
+        <Win32>
+          <GraphicApplication Value="True"/>
+        </Win32>
+      </Options>
     </Linking>
   </CompilerOptions>
   <Debugging>

applications/lazstats/source/forms/simulations/distribunit.lfm

@@ -2,12 +2,12 @@ object DistribFrm: TDistribFrm
   Left = 420
   Height = 432
   Top = 215
-  Width = 687
+  Width = 701
   HelpType = htKeyword
   HelpKeyword = 'html/DistributionPlotsandCriticalValu.htm'
   Caption = 'Distributions'
   ClientHeight = 432
-  ClientWidth = 687
+  ClientWidth = 701
   OnActivate = FormActivate
   OnShow = FormShow
   Position = poMainFormCenter
@@ -19,7 +19,7 @@ object DistribFrm: TDistribFrm
     AnchorSideRight.Side = asrBottom
     AnchorSideBottom.Control = Owner
     AnchorSideBottom.Side = asrBottom
-    Left = 624
+    Left = 638
     Height = 25
     Top = 401
     Width = 55
@@ -35,7 +35,7 @@ object DistribFrm: TDistribFrm
   object ComputeBtn: TButton
     AnchorSideTop.Control = CloseBtn
     AnchorSideRight.Control = CloseBtn
-    Left = 540
+    Left = 554
     Height = 25
     Top = 401
     Width = 76
@@ -50,7 +50,7 @@ object DistribFrm: TDistribFrm
   object ResetBtn: TButton
     AnchorSideTop.Control = CloseBtn
     AnchorSideRight.Control = ComputeBtn
-    Left = 478
+    Left = 492
     Height = 25
     Top = 401
     Width = 54
@@ -72,7 +72,7 @@ object DistribFrm: TDistribFrm
     Left = 0
     Height = 8
     Top = 385
-    Width = 687
+    Width = 701
     Anchors = [akLeft, akRight, akBottom]
     Shape = bsBottomLine
   end
@@ -84,7 +84,7 @@ object DistribFrm: TDistribFrm
     Left = 8
     Height = 377
     Top = 8
-    Width = 479
+    Width = 454
     Anchors = [akTop, akLeft, akRight, akBottom]
     BorderSpacing.Left = 8
     BorderSpacing.Top = 8
@@ -92,7 +92,7 @@ object DistribFrm: TDistribFrm
     BevelOuter = bvNone
     BorderStyle = bsSingle
     ClientHeight = 373
-    ClientWidth = 475
+    ClientWidth = 450
     Color = clWhite
     ParentColor = False
     TabOrder = 3
@@ -100,7 +100,7 @@ object DistribFrm: TDistribFrm
       Left = 6
       Height = 361
       Top = 6
-      Width = 463
+      Width = 438
       AxisList = <      
         item
           Grid.Color = clSilver
@@ -146,6 +146,12 @@ object DistribFrm: TDistribFrm
       end
       object VertLineSeries: TLineSeries
         Active = False
+        LinePen.Color = clRed
+        LinePen.Style = psDot
+      end
+      object HorLineSeries: TLineSeries
+        LinePen.Color = clRed
+        LinePen.Style = psDot
       end
     end
   end
@@ -181,42 +187,42 @@ object DistribFrm: TDistribFrm
     AnchorSideRight.Control = Owner
     AnchorSideRight.Side = asrBottom
     AnchorSideBottom.Control = Bevel1
-    Left = 499
+    Left = 474
     Height = 377
     Top = 8
-    Width = 180
+    Width = 219
     Anchors = [akTop, akRight, akBottom]
     AutoSize = True
     BorderSpacing.Top = 8
     BorderSpacing.Right = 8
     BevelOuter = bvNone
     ClientHeight = 377
-    ClientWidth = 180
+    ClientWidth = 219
     TabOrder = 6
     object GroupBox1: TGroupBox
       AnchorSideLeft.Control = ParameterPanel
       AnchorSideTop.Control = ParameterPanel
       AnchorSideRight.Side = asrBottom
       Left = 0
-      Height = 136
+      Height = 175
       Top = 0
-      Width = 180
+      Width = 219
       AutoSize = True
-      Caption = 'Plot Distribution:'
+      Caption = 'Plot Distribution'
       ChildSizing.LeftRightSpacing = 16
       ChildSizing.TopBottomSpacing = 8
       ChildSizing.VerticalSpacing = 8
-      ChildSizing.EnlargeVertical = crsHomogenousSpaceResize
+      ChildSizing.EnlargeVertical = crsScaleChilds
       ChildSizing.Layout = cclLeftToRightThenTopToBottom
       ChildSizing.ControlsPerLine = 1
-      ClientHeight = 116
+      ClientHeight = 155
-      ClientWidth = 176
+      ClientWidth = 215
       TabOrder = 0
       object NDChk: TRadioButton
         Left = 16
         Height = 19
         Top = 8
-        Width = 144
+        Width = 183
         Caption = 'Normal Distribution'
         OnClick = DistributionClick
         TabOrder = 0
@@ -225,8 +231,8 @@ object DistribFrm: TDistribFrm
         Left = 16
         Height = 19
         Top = 35
-        Width = 144
+        Width = 183
-        Caption = 'Student t Distribution'
+        Caption = 'Student t Distribution (1-sided)'
         OnClick = DistributionClick
         TabOrder = 3
       end
@@ -234,7 +240,7 @@ object DistribFrm: TDistribFrm
         Left = 16
         Height = 19
         Top = 62
-        Width = 144
+        Width = 183
         Caption = 'Central F Distribution'
         OnClick = DistributionClick
         TabOrder = 2
@@ -243,11 +249,28 @@ object DistribFrm: TDistribFrm
         Left = 16
         Height = 19
         Top = 89
-        Width = 144
+        Width = 183
         Caption = 'Chi-Square Distribution'
         OnClick = DistributionClick
         TabOrder = 1
       end
+      object Bevel2: TBevel
+        Left = 16
+        Height = 4
+        Top = 116
+        Width = 183
+        Constraints.MaxHeight = 4
+        Shape = bsBottomLine
+      end
+      object CumulativeChk: TCheckBox
+        Left = 16
+        Height = 19
+        Top = 128
+        Width = 183
+        Caption = 'Cumulative'
+        OnChange = CumulativeChkChange
+        TabOrder = 4
+      end
     end
     object GroupBox2: TGroupBox
       AnchorSideLeft.Control = GroupBox1
@@ -256,21 +279,22 @@ object DistribFrm: TDistribFrm
       AnchorSideRight.Control = GroupBox1
       AnchorSideRight.Side = asrBottom
       Left = 0
-      Height = 140
+      Height = 107
-      Top = 152
+      Top = 191
-      Width = 180
+      Width = 219
       Anchors = [akTop, akLeft, akRight]
+      AutoSize = True
       BorderSpacing.Top = 16
       BorderSpacing.Bottom = 12
       Caption = 'Parameters'
-      ClientHeight = 120
+      ClientHeight = 87
-      ClientWidth = 176
+      ClientWidth = 215
       TabOrder = 1
       object AlphaLabel: TLabel
         AnchorSideTop.Control = AlphaEdit
         AnchorSideTop.Side = asrCenter
         AnchorSideRight.Control = AlphaEdit
-        Left = 29
+        Left = 68
         Height = 15
         Top = 6
         Width = 84
@@ -283,7 +307,7 @@ object DistribFrm: TDistribFrm
         AnchorSideTop.Control = DF1Edit
         AnchorSideTop.Side = asrCenter
         AnchorSideRight.Control = DF1Edit
-        Left = 22
+        Left = 61
         Height = 15
         Top = 33
         Width = 91
@@ -297,7 +321,7 @@ object DistribFrm: TDistribFrm
         AnchorSideTop.Control = DF2Edit
         AnchorSideTop.Side = asrCenter
         AnchorSideRight.Control = DF2Edit
-        Left = 22
+        Left = 61
         Height = 15
         Top = 60
         Width = 91
@@ -307,25 +331,11 @@ object DistribFrm: TDistribFrm
         Caption = 'Deg. Freedom (2)'
         ParentColor = False
       end
-      object MeanLabel: TLabel
-        AnchorSideTop.Control = MeanEdit
-        AnchorSideTop.Side = asrCenter
-        AnchorSideRight.Control = MeanEdit
-        Left = 83
-        Height = 15
-        Top = 93
-        Width = 30
-        Anchors = [akTop, akRight]
-        BorderSpacing.Right = 8
-        Caption = 'Mean'
-        ParentColor = False
-        Visible = False
-      end
       object AlphaEdit: TEdit
         AnchorSideTop.Control = GroupBox2
         AnchorSideRight.Control = GroupBox2
         AnchorSideRight.Side = asrBottom
-        Left = 121
+        Left = 160
         Height = 23
         Top = 2
         Width = 43
@@ -341,7 +351,7 @@ object DistribFrm: TDistribFrm
         AnchorSideTop.Side = asrBottom
         AnchorSideRight.Control = AlphaEdit
         AnchorSideRight.Side = asrBottom
-        Left = 121
+        Left = 160
         Height = 23
         Top = 29
         Width = 43
@@ -351,40 +361,36 @@ object DistribFrm: TDistribFrm
         TabOrder = 1
         Text = 'DF1Edit'
       end
-      object MeanEdit: TEdit
-        AnchorSideTop.Control = DF2Edit
-        AnchorSideTop.Side = asrBottom
-        AnchorSideRight.Control = AlphaEdit
-        AnchorSideRight.Side = asrBottom
-        Left = 121
-        Height = 23
-        Top = 89
-        Width = 43
-        Alignment = taRightJustify
-        Anchors = [akTop, akRight]
-        BorderSpacing.Top = 4
-        BorderSpacing.Bottom = 8
-        TabOrder = 3
-        Text = 'MeanEdit'
-        Visible = False
-      end
       object DF2Edit: TEdit
         AnchorSideTop.Control = DF1Edit
         AnchorSideTop.Side = asrBottom
         AnchorSideRight.Control = AlphaEdit
         AnchorSideRight.Side = asrBottom
-        Left = 121
+        Left = 160
         Height = 23
         Top = 56
         Width = 43
         Alignment = taRightJustify
         Anchors = [akTop, akRight]
         BorderSpacing.Top = 4
-        BorderSpacing.Bottom = 10
+        BorderSpacing.Bottom = 8
         TabOrder = 2
         Text = 'DF2Edit'
       end
     end
+    object ShowCriticalValuesChk: TCheckBox
+      AnchorSideLeft.Control = ParameterPanel
+      AnchorSideTop.Control = GroupBox2
+      AnchorSideTop.Side = asrBottom
+      Left = 0
+      Height = 19
+      Top = 310
+      Width = 123
+      Caption = 'Show critical values'
+      Checked = True
+      State = cbChecked
+      TabOrder = 2
+    end
   end
   object SavePictureDialog: TSavePictureDialog
     Filter = 'Graphic (*.png;*.bmp;*.jpeg;*.jpg;*.jpe;*.jfif;*.svg)|*.png;*.bmp;*.jpeg;*.jpg;*.jpe;*.jfif;*.svg|Portable Network Graphic (*.png)|*.png|Bitmaps (*.bmp)|*.bmp|Joint Picture Expert Group (*.jpeg;*.jpg;*.jpe;*.jfif)|*.jpeg;*.jpg;*.jpe;*.jfif|Scaleable Vector Graphic (*.svg)|*.svg|All Files (*.*)|*.*'

applications/lazstats/source/forms/simulations/distribunit.pas

@@ -23,7 +23,11 @@ type
   TDistribFrm = class(TForm)
     AlphaEdit: TEdit;
     Bevel1: TBevel;
+    Bevel2: TBevel;
+    ShowCriticalValuesChk: TCheckBox;
+    HorLineSeries: TLineSeries;
     ChartToolset: TChartToolset;
+    CumulativeChk: TCheckBox;
     PanDragTool: TPanDragTool;
     tChk: TRadioButton;
     ZoomDragTool: TZoomDragTool;
@@ -39,7 +43,6 @@ type
     DF1Edit: TEdit;
     DF2Edit: TEdit;
     FChk: TRadioButton;
-    MeanEdit: TEdit;
     NDChk: TRadioButton;
     ChartPanel: TPanel;
     ResetBtn: TButton;
@@ -49,15 +52,19 @@ type
     AlphaLabel: TLabel;
     DF1Label: TLabel;
     DF2Label: TLabel;
-    MeanLabel: TLabel;
     GroupBox1: TGroupBox;
     procedure ComputeBtnClick(Sender: TObject);
+    procedure CumulativeChkChange(Sender: TObject);
     procedure FormActivate(Sender: TObject);
     procedure FormShow(Sender: TObject);
-    procedure CalcChiSq(const AX: Double; out AY: Double);
+    procedure CalcChi2(const AX: Double; out AY: Double);
+    procedure CalcChi2_Cumulative(const AX: Double; out AY: Double);
     procedure CalcF(const AX: Double; out AY: Double);
+    procedure CalcF_Cumulative(const AX: Double; out AY: Double);
     procedure CalcND(const AX: Double; out AY: Double);
-    procedure Calct(const AX: Double; out AY: Double);
+    procedure CalcND_Cumulative(const AX: Double; out AY: Double);
+    procedure CalcT(const AX: Double; out AY: Double);
+    procedure CalcT_Cumulative(const AX: Double; out AY: Double);
     procedure DistributionClick(Sender: TObject);
     procedure PrintBtnClick(Sender: TObject);
     procedure ResetBtnClick(Sender: TObject);
@@ -67,7 +74,7 @@ type
     DF1: Integer;
     DF2: Integer;
     procedure NormalDistPlot;
-    procedure ChiPlot;
+    procedure Chi2Plot;
     procedure FPlot;
     procedure tPlot;
 
@@ -97,7 +104,6 @@ begin
   AlphaEdit.Text := FormatFloat('0.00', DEFAULT_ALPHA_LEVEL);
   DF1Edit.Text := '';
   DF2Edit.Text := '';
-  MeanEdit.Text := '';
   GroupBox2.Enabled := false;
   FuncSeries.OnCalculate := nil;
   VertLineSeries.Active := false;
@@ -105,6 +111,7 @@ begin
   Chart.BottomAxis.Title.Caption := 'Scale';
 end;
 
+
 procedure TDistribFrm.SaveBtnClick(Sender: TObject);
 var
   ext: String;
@@ -121,31 +128,67 @@ begin
   end;
 end;
 
+
 procedure TDistribFrm.FormShow(Sender: TObject);
 begin
   ResetBtnClick(self);
 end;
 
+
 procedure TDistribFrm.CalcF(const AX: Double; out AY: Double);
 begin
   AY := FDensity(AX, DF1, DF2);
 end;
 
+
+procedure TDistribFrm.CalcF_Cumulative(const AX: Double; out AY: Double);
+begin
+  AY := 1.0 - ProbF(AX, DF1, DF2);
+end;
+
+
 procedure TDistribFrm.CalcND(const AX: Double; out AY: Double);
 begin
   AY := 1.0 / sqrt(TWO_PI) * exp(-sqr(AX)/ 2.0);
 end;
 
-procedure TDistribFrm.CalcChiSq(const AX: Double; out AY: Double);
+
+procedure TDistribFrm.CalcND_Cumulative(const AX: Double; out AY: Double);
+begin
+  // AY := ProbZ(AX);  -- very slow
+  AY := NormalDist(AX);  // borrowed from NumLib
+end;
+
+
+procedure TDistribFrm.CalcChi2(const AX: Double; out AY: Double);
 begin
   AY := Chi2Density(AX, DF1);
 end;
 
+
+procedure TDistribFrm.CalcChi2_Cumulative(const AX: Double; out AY: Double);
+begin
+  AY := ChiSquaredProb(AX, DF1);
+end;
+
+
 procedure TDistribFrm.Calct(const AX: Double; out AY: Double);
 begin
   AY := tDensity(AX, DF1);
 end;
 
+
+procedure TDistribFrm.CalcT_Cumulative(const AX: Double; out AY: Double);
+const
+  ONE_SIDED = true;
+begin
+  if AX < 0 then
+    AY := tDist(-AX, DF1, ONE_SIDED)
+  else
+    AY := 1.0 - tDist(AX, DF1, ONE_SIDED);
+end;
+
+
 procedure TDistribFrm.DistributionClick(Sender: TObject);
 var
   rb: TRadiobutton;
@@ -162,28 +205,9 @@ begin
 
   DF2Edit.Enabled := (rb = FChk) and rb.Checked;
   DF2Label.Enabled := DF2Edit.Enabled;
-
-  MeanEdit.Enabled := false;
-  MeanLabel.Enabled := false;
-  {
-
-   if NDChk.Checked then
-   begin
-     GroupBox2.Enabled := true;
-     AlphaLabel.Enabled := true;
-     AlphaEdit.Enabled := true;
-     DF1Edit.Enabled := false;
-     DF1Label.Enabled := false;
-     DF2Label.Enabled := false;
-     MeanLabel.Enabled := false;
-     DF2Edit.Enabled := false;
-     MeanEdit.Enabled := false;
-   end
-   else
-     GroupBox2.Enabled := false;
-     }
 end;
 
+
 procedure TDistribFrm.PrintBtnClick(Sender: TObject);
 const
   MARGIN = 10;
@@ -212,6 +236,7 @@ begin
   end;
 end;
 
+
 procedure TDistribFrm.ComputeBtnClick(Sender: TObject);
 var
   msg: String;
@@ -240,7 +265,7 @@ begin
 
   if ChiChk.Checked then
   begin
-    ChiPlot();
+    Chi2Plot();
     ok := true;
   end;
 
@@ -254,13 +279,23 @@ begin
     MessageDlg('Please select a distribution.', mtError, [mbOK], 0);
 end;
 
+procedure TDistribFrm.CumulativeChkChange(Sender: TObject);
+begin
+  if CumulativeChk.Checked then
+    Chart.LeftAxis.Title.Caption := 'Cumulative probability'
+  else
+    Chart.LeftAxis.Title.Caption := 'Probability density';
+end;
+
+
 procedure TDistribFrm.NormalDistPlot;
 var
   alpha: Double;
-  zMax, zCrit, pCrit: Double;
+  zMax, zMin, zCrit, pCrit: Double;
 begin
   alpha := StrToFloat(AlphaEdit.Text);
   zMax := InverseZ(0.9999);
+  zMin := -zMax;
   zCrit := inversez(1.0 - alpha);
   CalcND(zCrit, pCrit);
 
@@ -270,28 +305,44 @@ begin
   Chart.Title.Text.Add(Format('Critical value = %.3f', [zCrit]));
   Chart.Title.Visible := true;
   Chart.BottomAxis.Title.Caption := 'z';
-  FuncSeries.Extent.XMin := -zMax;
+  FuncSeries.Extent.XMin := zMin;
-  FuncSeries.Extent.XMax := +zMax;
+  FuncSeries.Extent.XMax := zMax;
   FuncSeries.Extent.UseXMin := true;
   FuncSeries.Extent.UseXMax := true;
-  FuncSeries.OnCalculate := @CalcND;
+  if CumulativeChk.Checked then
+    FuncSeries.OnCalculate := @CalcND_Cumulative
+  else
+    FuncSeries.OnCalculate := @CalcND;
   FuncSeries.DomainExclusions.Clear;
-  VertLineSeries.Clear;
+
-  VertLineSeries.AddXY(zCrit, 0);
+  VertlineSeries.Clear;
-  VertLineSeries.AddXY(zCrit, pCrit);
+  if CumulativeChk.Checked then
-  VertLineSeries.Active := true;
+  begin
+    HorLineSeries.Clear;
+    HorLineSeries.AddXY(zMin, 1.0 - alpha);
+    HorLineSeries.AddXY(zCrit, 1.0 - alpha);
+    VertlineSeries.AddXY(zCrit, 1.0 - alpha);
+    VertLineSeries.AddXY(zCrit, 0);
+  end else
+  begin
+    VertLineSeries.AddXY(zCrit, 0);
+    VertLineSeries.AddXY(zCrit, pCrit);
+  end;
+  HorLineSeries.Active := ShowCriticalValuesChk.Checked and CumulativeChk.Checked;
+  VertLineSeries.Active := ShowCriticalValuesChk.Checked;
 end;
 
-procedure TDistribFrm.ChiPlot;
+
+procedure TDistribFrm.Chi2Plot;
 var
   alpha: Double;
-  Chi2Max, Chi2Crit, pCrit: Double;
+  chi2Max, chi2Crit, pCrit: Double;
 begin
   alpha := StrToFloat(AlphaEdit.Text);
   DF1 := StrToInt(DF1Edit.Text);
-  Chi2Max := InverseChi(0.9999, DF1);
+  chi2Max := InverseChi(0.9999, DF1);
-  Chi2Crit := InverseChi(1.0 - alpha, DF1);
+  chi2Crit := InverseChi(1.0 - alpha, DF1);
-  CalcChiSq(Chi2Crit, pCrit);
+  CalcChi2(chi2Crit, pCrit);
 
   Chart.Title.Text.Clear;
   Chart.Title.Text.Add('<b>Chi-Squared Distribution</b>');
@@ -300,17 +351,32 @@ begin
   Chart.Title.Visible := true;
   Chart.BottomAxis.Title.Caption := '&chi;<sup>2</sup>';
   FuncSeries.Extent.XMin := 0;
-  FuncSeries.Extent.XMax := Chi2Max;
+  FuncSeries.Extent.XMax := chi2Max;
   FuncSeries.Extent.UseXMin := true;
   FuncSeries.Extent.UseXMax := true;
-  FuncSeries.OnCalculate := @CalcChiSq;
+  if CumulativeChk.Checked then
+    FuncSeries.OnCalculate := @CalcChi2_Cumulative
+  else
+    FuncSeries.OnCalculate := @CalcChi2;
   FuncSeries.DomainExclusions.AddRange(-Infinity, 0, [ioOpenEnd]);
+
   VertLineSeries.Clear;
-  VertLineSeries.AddXY(Chi2Crit, 0);
+  if CumulativeChk.Checked then begin
-  VertLineSeries.AddXY(Chi2Crit, pCrit);
+    HorLineSeries.Clear;
-  VertLineSeries.Active := true;
+    HorLineSeries.AddXY(0, 1.0 - alpha);
+    HorLineSeries.AddXY(chi2Crit, 1.0 - alpha);
+    VertlineSeries.AddXY(chi2Crit, 1.0 - alpha);
+    VertLineSeries.AddXY(chi2Crit, 0);
+  end else
+  begin
+    VertLineSeries.AddXY(chi2Crit, 0);
+    VertLineSeries.AddXY(chi2Crit, pCrit);
+  end;
+  HorLineSeries.Active := ShowCriticalValuesChk.Checked and CumulativeChk.Checked;
+  VertLineSeries.Active := ShowCriticalValuesChk.Checked;
 end;
 
+
 procedure TDistribFrm.FPlot;
 var
   alpha: Double;
@@ -333,22 +399,39 @@ begin
   FuncSeries.Extent.XMax := FMax;
   FuncSeries.Extent.UseXMin := true;
   FuncSeries.Extent.UseXMax := true;
-  FuncSeries.OnCalculate := @CalcF;
+  if CumulativeChk.Checked then
+    FuncSeries.OnCalculate := @CalcF_Cumulative
+  else
+    FuncSeries.OnCalculate := @CalcF;
   FuncSeries.DomainExclusions.AddRange(-Infinity, 0, [ioOpenEnd]);
+
   VertLineSeries.Clear;
-  VertLineSeries.AddXY(FCrit, 0);
+  if CumulativeChk.Checked then
-  VertLineSeries.AddXY(FCrit, pCrit);
+  begin
-  VertLineSeries.Active := true;
+    HorLineSeries.Clear;
+    HorLineSeries.AddXY(0, 1.0 - alpha);
+    HorLineSeries.AddXY(FCrit, 1.0 - alpha);
+    VertLineSeries.AddXY(FCrit, 1.0 - alpha);
+    VertLineSeries.AddXY(FCrit, 0);
+  end else
+  begin
+    VertLineSeries.AddXY(FCrit, 0);
+    VertLineSeries.AddXY(FCrit, pCrit);
+  end;
+  HorLineSeries.Active := ShowCriticalValuesChk.Checked and CumulativeChk.Checked;
+  VertLineSeries.Active := ShowCriticalValuesChk.Checked;
 end;
 
+
 procedure TDistribFrm.tPlot;
 var
   alpha: Double;
-  tMax, tCrit, pCrit: Double;
+  tMin, tMax, tCrit, pCrit: Double;
 begin
   alpha := StrToFloat(AlphaEdit.Text);
   DF1 := StrToInt(DF1Edit.Text);
   tMax := Inverset(0.9999, DF1);
+  tMin := -tMax;
   tCrit := Inverset(1.0 - alpha, DF1);
   Calct(tCrit, pCrit);
 
@@ -358,18 +441,34 @@ begin
   Chart.Title.Text.Add(Format('Critical value = %.3f', [tCrit]));
   Chart.Title.Visible := true;
   Chart.BottomAxis.Title.Caption := 't';
-  FuncSeries.Extent.XMin := -tmax;
+  FuncSeries.Extent.XMin := tMin;
   FuncSeries.Extent.XMax := tMax;
   FuncSeries.Extent.UseXMin := true;
   FuncSeries.Extent.UseXMax := true;
-  FuncSeries.OnCalculate := @Calct;
+  if CumulativeChk.Checked then
+    FuncSeries.OnCalculate := @CalcT_Cumulative
+  else
+    FuncSeries.OnCalculate := @CalcT;
   FuncSeries.DomainExclusions.Clear;
+
   VertLineSeries.Clear;
-  VertLineSeries.AddXY(tCrit, 0);
+  if CumulativeChk.Checked then
-  VertLineSeries.AddXY(tCrit, pCrit);
+  begin
-  VertLineSeries.Active := true;
+    HorLineSeries.Clear;
+    HorLineSeries.AddXY(tMin, 1.0 - alpha);
+    HorLineSeries.AddXY(tCrit, 1.0 - alpha);
+    VertLineSeries.AddXY(tCrit, 1.0 - alpha);
+    VertLineSeries.AddXY(tCrit, 0);
+  end else
+  begin
+    VertLineSeries.AddXY(tCrit, 0);
+    VertLineSeries.AddXY(tCrit, pCrit);
+  end;
+  HorLineSeries.Active := ShowCriticalValuesChk.Checked and CumulativeChk.Checked;
+  VertLineSeries.Active := ShowCriticalValuesChk.Checked;
 end;
 
+
 procedure TDistribFrm.FormActivate(Sender: TObject);
 var
   w: Integer;

applications/lazstats/source/units/functionslib.pas

@@ -980,16 +980,15 @@ begin
 end;
 //-------------------------------------------------------------------
 
-function probt(t,df1 : double) : double;
+// Returns the probability corresponding to a two-tailed t test.
+function ProbT(t, df1: double): double;
 var
-   F, prob : double;
+  F, prob: double;
 begin
-    // Returns the probability corresponding to a two-tailed t test.
+  F := t * t;
-    F := t * t;
+  prob := ProbF(F, 1.0, df1);
-    prob := probf(F,1.0,df1);
+  Result := prob;
-    Result := prob;
 end;
-//------------------------------------------------------------------------
 
 function inverset(Probt, DF : double) : double;
 var

applications/lazstats/source/units/mathunit.pas

@@ -9,6 +9,10 @@ interface
 uses
   Classes, SysUtils;
 
+function erf(x: Double): Double;
+function erfc(x: Double) : Double;
+function NormalDist(x: Double): Double;
+
 function Beta(a, b: Double): Extended;
 function BetaI(a,b,x: Double): Extended;
 
@@ -26,6 +30,104 @@ implementation
 uses
   Math;
 
+// Calculates the error function
+//                              /x
+//       erf(x) = 2/sqrt(pi) * | exp(-t²) dt
+//                            /0
+// borrowed from NumLib
+function erf(x: Double): Double;
+const
+  xup = 6.25;
+  SQRT_PI = 1.7724538509055160;
+  c: array[1..18] of Double = (
+       1.9449071068178803e0,  4.20186582324414e-2, -1.86866103976769e-2,
+       5.1281061839107e-3,   -1.0683107461726e-3,   1.744737872522e-4,
+      -2.15642065714e-5,      1.7282657974e-6,     -2.00479241e-8,
+      -1.64782105e-8,         2.0008475e-9,         2.57716e-11,
+      -3.06343e-11,           1.9158e-12,           3.703e-13,
+      -5.43e-14,             -4.0e-15,              1.2e-15
+  );
+  d: array[1..17] of Double = (
+       1.4831105640848036e0, -3.010710733865950e-1, 6.89948306898316e-2,
+      -1.39162712647222e-2,   2.4207995224335e-3,  -3.658639685849e-4,
+       4.86209844323e-5,     -5.7492565580e-6,      6.113243578e-7,
+      -5.89910153e-8,         5.2070091e-9,        -4.232976e-10,
+       3.18811e-11,          -2.2361e-12,           1.467e-13,
+      -9.0e-15,               5.0e-16
+  );
+var
+  t, s, s1, s2, x2: Double;
+  bovc, bovd, j: Integer;
+  sgn: Integer;
+begin
+  bovc := SizeOf(c) div SizeOf(Double);
+  bovd := SizeOf(d) div SizeOf(Double);
+  t := abs(x);
+  if t <= 2 then
+  begin
+    x2 := sqr(x) - 2;
+    s1 := d[bovd];
+    s2 := 0;
+    j := bovd - 1;
+    s := x2*s1 - s2 + d[j];
+    while j > 1 do
+    begin
+      s2 := s1;
+      s1 := s;
+      j := j-1;
+      s := x2*s1 - s2 + d[j];
+    end;
+    Result := (s - s2) * x / 2;
+  end else
+  if t < xup then
+  begin
+    x2 := 2 - 20 / (t+3);
+    s1 := c[bovc];
+    s2 := 0;
+    j := bovc - 1;
+    s := x2*s1 - s2 + c[j];
+    while j > 1 do
+    begin
+      s2 := s1;
+      s1 := s;
+      j := j-1;
+      s := x2*s1 - s2 + c[j];
+    end;
+    x2 := ((s-s2) / (2*t)) * exp(-sqr(x)) / SQRT_PI;
+    if x < 0 then sgn := -1 else sgn := +1;
+    Result := (1 - x2) * sgn
+  end
+  else
+  if x < 0 then
+    Result := -1.0
+  else
+    Result := +1.0;
+end;
+
+
+{ calculates the complementary error function erfc(x) = 1 - erf(x) }
+function erfc(x: Double) : Double;
+begin
+  Result := 1.0 - erf(x);
+end;
+
+
+// Cumulative normal distribution
+// x = -INF ... INF --> 0 ... 1
+function NormalDist(x: Double): Double;
+const
+  SQRT2 = sqrt(2.0);
+begin
+  if x > 0 then
+    Result := (erf(x / SQRT2) + 1) * 0.5
+  else
+  if x < 0 then
+    Result := (1.0 - erf(-x / SQRT2)) * 0.5
+  else
+    Result := 0;
+end;
+
+
 function Beta(a, b: Double): Extended;
 begin
   if (a > 0) and (b > 0) then