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Lazstats: Massive refactoring of DescriptiveUnits: Move calculation to new TDescriptiveStats class. More user-friendly interface.

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git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7730 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
2020-10-02 17:14:33 +00:00
parent 0175c44fa5
commit c25230eb89
6 changed files with 682 additions and 338 deletions
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5
applications/lazstats/source/LazStats.lpi
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@ -1558,11 +1558,6 @@
<DebugInfoType Value="dsDwarf2"/> <DebugInfoType Value="dsDwarf2"/>
</Debugging> </Debugging>
<LinkSmart Value="True"/> <LinkSmart Value="True"/>
<Options>
<Win32>
<GraphicApplication Value="True"/>
</Win32>
</Options>
</Linking> </Linking>
</CompilerOptions> </CompilerOptions>
<Debugging> <Debugging>

87
applications/lazstats/source/forms/analysis/descriptive/descriptiveunit.lfm
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@ -1,37 +1,45 @@
inherited DescriptiveFrm: TDescriptiveFrm inherited DescriptiveFrm: TDescriptiveFrm
Left = 526 Left = 526
Height = 384 Height = 432
Top = 202 Top = 202
Width = 900 Width = 900
HelpType = htKeyword HelpType = htKeyword
HelpKeyword = 'html/DistributionStatistics.htm' HelpKeyword = 'html/DistributionStatistics.htm'
Caption = 'Descriptive Statistics' Caption = 'Descriptive Statistics'
ClientHeight = 384 ClientHeight = 432
ClientWidth = 900 ClientWidth = 900
inherited ParamsPanel: TPanel inherited ParamsPanel: TPanel
Left = 16 Left = 16
Height = 352 Height = 400
Top = 16 Top = 16
Width = 322 Width = 322
BorderSpacing.Around = 8 BorderSpacing.Around = 8
ClientHeight = 352 ClientHeight = 400
ClientWidth = 322 ClientWidth = 322
inherited CloseBtn: TButton inherited CloseBtn: TButton
Left = 267
Top = 375
TabOrder = 9 TabOrder = 9
end end
inherited ComputeBtn: TButton inherited ComputeBtn: TButton
AnchorSideBottom.Control = ParamsPanel AnchorSideBottom.Control = ParamsPanel
AnchorSideBottom.Side = asrBottom AnchorSideBottom.Side = asrBottom
Left = 184
Top = 375
TabOrder = 10 TabOrder = 10
end end
inherited ResetBtn: TButton inherited ResetBtn: TButton
Left = 122
Top = 375
TabOrder = 8 TabOrder = 8
end end
inherited HelpBtn: TButton inherited HelpBtn: TButton
Left = 63
Top = 375
TabOrder = 7 TabOrder = 7
end end
inherited ButtonBevel: TBevel inherited ButtonBevel: TBevel
Top = 311 Top = 359
Width = 322 Width = 322
end end
object Label2: TLabel[5] object Label2: TLabel[5]
@ -51,7 +59,7 @@ inherited DescriptiveFrm: TDescriptiveFrm
AnchorSideRight.Control = AllBtn AnchorSideRight.Control = AllBtn
AnchorSideBottom.Control = OptionsGroup AnchorSideBottom.Control = OptionsGroup
Left = 0 Left = 0
Height = 183 Height = 202
Top = 17 Top = 17
Width = 130 Width = 130
Anchors = [akTop, akLeft, akRight, akBottom] Anchors = [akTop, akLeft, akRight, akBottom]
@ -84,7 +92,7 @@ inherited DescriptiveFrm: TDescriptiveFrm
AnchorSideBottom.Control = VarList AnchorSideBottom.Control = VarList
AnchorSideBottom.Side = asrBottom AnchorSideBottom.Side = asrBottom
Left = 192 Left = 192
Height = 183 Height = 202
Top = 17 Top = 17
Width = 130 Width = 130
Anchors = [akTop, akLeft, akRight, akBottom] Anchors = [akTop, akLeft, akRight, akBottom]
@ -149,7 +157,7 @@ inherited DescriptiveFrm: TDescriptiveFrm
AnchorSideRight.Control = CIEdit AnchorSideRight.Control = CIEdit
Left = 0 Left = 0
Height = 15 Height = 15
Top = 292 Top = 311
Width = 174 Width = 174
BorderSpacing.Right = 8 BorderSpacing.Right = 8
Caption = 'Confidence Interval for the Mean' Caption = 'Confidence Interval for the Mean'
@ -161,7 +169,7 @@ inherited DescriptiveFrm: TDescriptiveFrm
AnchorSideBottom.Control = CIEdit AnchorSideBottom.Control = CIEdit
Left = 0 Left = 0
Height = 72 Height = 72
Top = 208 Top = 227
Width = 306 Width = 306
Anchors = [akLeft, akBottom] Anchors = [akLeft, akBottom]
AutoSize = True AutoSize = True
@ -197,7 +205,7 @@ inherited DescriptiveFrm: TDescriptiveFrm
Caption = 'z Scores to Grid' Caption = 'z Scores to Grid'
TabOrder = 1 TabOrder = 1
end end
object PcntileChk: TCheckBox object PercentileChk: TCheckBox
AnchorSideTop.Side = asrBottom AnchorSideTop.Side = asrBottom
Left = 12 Left = 12
Height = 19 Height = 19
@ -208,7 +216,7 @@ inherited DescriptiveFrm: TDescriptiveFrm
Caption = 'Show Percentile Ranks' Caption = 'Show Percentile Ranks'
TabOrder = 2 TabOrder = 2
end end
object AllQrtilesChk: TCheckBox object AllQuartilesChk: TCheckBox
AnchorSideTop.Side = asrBottom AnchorSideTop.Side = asrBottom
Left = 174 Left = 174
Height = 19 Height = 19
@ -224,29 +232,66 @@ inherited DescriptiveFrm: TDescriptiveFrm
AnchorSideLeft.Control = Label1 AnchorSideLeft.Control = Label1
AnchorSideLeft.Side = asrBottom AnchorSideLeft.Side = asrBottom
AnchorSideRight.Side = asrBottom AnchorSideRight.Side = asrBottom
AnchorSideBottom.Control = DecPlacesEdit
Left = 182 Left = 182
Height = 23 Height = 23
Top = 288 Top = 307
Width = 41 Width = 50
Alignment = taRightJustify Alignment = taRightJustify
Anchors = [akLeft, akBottom] Anchors = [akLeft, akBottom]
BorderSpacing.Left = 8 BorderSpacing.Left = 8
TabOrder = 6 TabOrder = 6
Text = '95.0' Text = '95.0'
end end
object DecPlacesEdit: TSpinEdit[15]
AnchorSideLeft.Control = CIEdit
AnchorSideTop.Side = asrBottom
AnchorSideRight.Control = CIEdit
AnchorSideRight.Side = asrBottom
AnchorSideBottom.Control = ButtonBevel
Left = 182
Height = 23
Top = 334
Width = 50
Alignment = taRightJustify
Anchors = [akLeft, akRight, akBottom]
BorderSpacing.Top = 4
BorderSpacing.Bottom = 2
MaxValue = 10
TabOrder = 11
Value = 3
end
object Label4: TLabel[16]
AnchorSideLeft.Control = Label1
AnchorSideTop.Control = DecPlacesEdit
AnchorSideTop.Side = asrCenter
Left = 0
Height = 15
Top = 338
Width = 79
Caption = 'Decimal places'
ParentColor = False
end
end end
inherited ParamsSplitter: TSplitter inherited ParamsSplitter: TSplitter
Left = 350 Left = 350
Height = 384 Height = 432
end end
object ReportPanel: TPanel[2] object PageControl: TPageControl[2]
Left = 355 Left = 359
Height = 384 Height = 416
Top = 0 Top = 8
Width = 545 Width = 533
ActivePage = ReportPage
Align = alClient Align = alClient
Anchors = [akTop, akLeft, akRight] BorderSpacing.Left = 4
BevelOuter = bvNone BorderSpacing.Top = 8
BorderSpacing.Right = 8
BorderSpacing.Bottom = 8
TabIndex = 0
TabOrder = 2 TabOrder = 2
object ReportPage: TTabSheet
Caption = 'Report'
end
end end
end end

803
applications/lazstats/source/forms/analysis/descriptive/descriptiveunit.pas
View File

@ -6,23 +6,73 @@ interface
uses uses
Classes, SysUtils, FileUtil, Forms, Controls, Graphics, Dialogs, Classes, SysUtils, FileUtil, Forms, Controls, Graphics, Dialogs,
StdCtrls, ExtCtrls, Buttons, StdCtrls, ExtCtrls, Buttons, Spin, ComCtrls, Grids,
MainUnit, Globals, FunctionsLib, BasicStatsReportFormUnit, MainUnit, Globals, FunctionsLib, ReportFrameUnit, BasicStatsReportFormUnit,
DataProcs, DictionaryUnit; DataProcs, DictionaryUnit;
type type
{ TDescriptiveFrm } { TDescriptiveStats }
TDescriptiveOption = (doAlternativeQuartiles, doPercentileRanks, doCasewiseDeletion);
TDescriptiveOptions = set of TDescriptiveOption;
TQuartileMethod = 1..8;
TQuartile = 1..3;
TDescriptiveStats = class
private
FDataGrid: TStringGrid;
FColIndex: Integer;
FConfLevel: Double; // usually 0.95
FColsSelected: IntDyneVec;
FMean, FStdErrorMean, FDeltaMean: Double;
FMin, FMax: Double;
FSum: Double;
FVariance, FStdDev: Double;
FSkew, FStdErrorSkew: Double;
FKurtosis, FStdErrorKurtosis: Double;
FFirstQuartile, FMedian, FThirdQuartile: Double;
FCategoryValues, FPercentiles: DblDyneVec;
FFreqValues: IntDyneVec;
FOptions: TDescriptiveOptions;
FNumCases: Integer;
FQuartiles: array[TQuartileMethod, TQuartile] of Double;
procedure Calc_AlternativeQuartiles(const AValues: DblDyneVec);
function Calc_DeltaMean(AStdErrorOfMean: Double): Double;
procedure Calc_Moments(const AValues: DblDyneVec; AMean: Double;
out M2, M3, M4: Double);
procedure Calc_Quartiles(const AValues: DblDyneVec; out Q1, Median, Q3: Double);
procedure Calc_Skew_Kurtosis(StdDev, M2, M3, M4: Double; ANumCases: Integer;
out Skew, StdErrorSkew, Kurtosis, StdErrorKurtosis: Double);
procedure Calc_Sum_SumOfSquares_Min_Max(const AValues: DblDyneVec;
out ASum, ASumOfSquares, AMin, AMax: Double);
procedure CollectValues(out AValues: DblDyneVec);
procedure PercentileRank(const AValues: DblDyneVec;
out ACategoryValues, APercentiles: DblDyneVec; out AFreq: IntDyneVec);
public
constructor Create(ADataGrid: TStringGrid; AColsSelected: IntDyneVec; AConfLevel: Double);
procedure Analyze(AColIndex: Integer; AOptions: TDescriptiveOptions);
procedure WriteToReport(AVarName: String; ADecPlaces: Integer; AReport: TStrings);
property Mean: Double read FMean;
property StdDev: Double read FStdDev;
// more can be added...
end;
{ TDescriptiveFrm }
TDescriptiveFrm = class(TBasicStatsReportForm) TDescriptiveFrm = class(TBasicStatsReportForm)
CaseChk: TCheckBox; CaseChk: TCheckBox;
DecPlacesEdit: TSpinEdit;
Label4: TLabel;
PageControl: TPageControl;
ReportPage: TTabSheet;
ZScoresToGridChk: TCheckBox; ZScoresToGridChk: TCheckBox;
AllQrtilesChk: TCheckBox; AllQuartilesChk: TCheckBox;
Label2: TLabel; Label2: TLabel;
Label3: TLabel; Label3: TLabel;
ReportPanel: TPanel; PercentileChk: TCheckBox;
PcntileChk: TCheckBox;
OptionsGroup: TGroupBox; OptionsGroup: TGroupBox;
InBtn: TBitBtn; InBtn: TBitBtn;
OutBtn: TBitBtn; OutBtn: TBitBtn;
@ -39,9 +89,9 @@ type
procedure VarListSelectionChange(Sender: TObject; {%H-}User: boolean); procedure VarListSelectionChange(Sender: TObject; {%H-}User: boolean);
private private
{ private declarations } function GetReportFrame(APageIndex: Integer): TReportFrame;
sum, variance, stddev, value, mean, min, max, range, skew, prob, df, CI : double; procedure zScoresToGrid(AColIndex: Integer; const AColsSelected: IntDyneVec;
kurtosis, z, semean, seskew, sekurtosis, deviation, devsqr, M2, M3, M4 : double; AMean, AStdDev: Double);
protected protected
procedure AdjustConstraints; override; procedure AdjustConstraints; override;
@ -49,6 +99,7 @@ type
procedure UpdateBtnStates; override; procedure UpdateBtnStates; override;
public public
constructor Create(AOwner: TComponent); override;
procedure Reset; override; procedure Reset; override;
end; end;
@ -61,15 +112,381 @@ implementation
{$R *.lfm} {$R *.lfm}
uses uses
Math; Math,
Utils;
{===============================================================================
* TDescriptiveStats
*-------------------------------------------------------------------------------
* TDescriptiveStats is a helper class which
* - does all the required calculations (Analyze) and
* - prepares the report for each variable (WriteToReport).
*==============================================================================}
constructor TDescriptiveStats.Create(ADataGrid: TStringGrid;
AColsSelected: IntDyneVec; AConfLevel: Double);
begin
inherited Create;
FDataGrid := ADataGrid;
FColsSelected := AColsSelected;
FConfLevel := AConfLevel;
end;
procedure TDescriptiveStats.Analyze(AColIndex: Integer; AOptions: TDescriptiveOptions);
var
SS: Double;
values: DblDyneVec;
M2, M3, M4: Double;
begin
FMean := NaN;
FVariance := NaN;
FStdDev := NaN;
FStdErrorMean := NaN;
FDeltaMean := NaN;
FSkew := NaN;
FStdErrorSkew := NaN;
FColIndex := AColIndex;
FOptions := AOptions;
CollectValues(values);
FNumCases := Length(values);
SortOnX(values);
Calc_Sum_SumOfSquares_Min_Max(values, FSum, SS, FMin, FMax);
if FNumCases > 0 then begin
FMean := FSum / FNumCases;
if FNumCases > 1 then
begin
FVariance := (SS - sqr(FSum) / FNumCases) / (FNumCases - 1);
FStdDev := sqrt(FVariance);
FStdErrorMean := sqrt(FVariance / FNumCases);
FDeltaMean := Calc_DeltaMean(FStdErrorMean);
end;
Calc_Moments(values, FMean, M2, M3, M4);
Calc_Skew_Kurtosis(FStdDev, M2, M3, M4, FNumCases, FSkew, FStdErrorSkew, FKurtosis, FStdErrorKurtosis);
Calc_Quartiles(values, FFirstQuartile, FMedian, FThirdQuartile);
if (doAlternativeQuartiles in FOptions) then
Calc_AlternativeQuartiles(values);
if (doPercentileRanks in FOptions) then
PercentileRank(values, FCategoryValues, FPercentiles, FFreqValues);
end;
end;
procedure TDescriptiveStats.Calc_AlternativeQuartiles(const AValues: DblDyneVec);
var
nCases: Integer;
q: TQuartile;
m: TQuartileMethod;
begin
nCases := Length(AValues);
for m := Low(TQuartileMethod) to High(TQuartileMethod) do
for q := Low(TQuartile) to High(TQuartile) do
FQuartiles[m, q] := Quartiles(m, 0.25*q, nCases, AValues);
end;
// Tolerance around the mean
function TDescriptiveStats.Calc_DeltaMean(AStdErrorOfMean: Double): Double;
var
alpha: Double;
confLev: Double;
DOF: Integer;
begin
alpha := (1 - FConfLevel) / 2;
confLev := 1 - alpha;
if FNumCases < 120 then
begin
DOF := FNumCases - 1;
Result := AStdErrorOfMean * InverseT(confLev, DOF);
end else
Result := AStdErrorOfMean * InverseZ(confLev);
end;
procedure TDescriptiveStats.Calc_Moments(const AValues: DblDyneVec;
AMean: Double; out M2, M3, M4: Double);
var
i: Integer;
dev, devSqr: Double;
begin
M2 := 0;
M3 := 0;
M4 := 0;
for i := 0 to High(AValues) do
begin
dev := AValues[i] - AMean;
devSqr := Sqr(dev);
M2 := M2 + devSqr;
M3 := M3 + dev * devSqr;
M4 := M4 + sqr(devSqr);
end;
end;
procedure TDescriptiveStats.Calc_Quartiles(const AValues: DblDyneVec;
out Q1, Median, Q3: Double);
var
n: Integer;
begin
n := Length(AValues);
Q1 := Quartiles(2, 0.25, n, AValues);
Median := Quartiles(2, 0.5, n, AValues);
Q3 := Quartiles(2, 0.75, n, AValues);
end;
procedure TDescriptiveStats.Calc_Skew_Kurtosis(StdDev, M2, M3, M4: Double;
ANumCases: Integer; out Skew, StdErrorSkew, Kurtosis, StdErrorKurtosis: Double);
var
num, denom: Double;
stdDev3, stdDev4: Double;
begin
Skew := NaN;
StdErrorSkew := NaN;
Kurtosis := NaN;
StdErrorKurtosis := NaN;
stdDev3 := StdDev * StdDev * StdDev;
stdDev4 := StdDev3 * StdDev;
if ANumCases > 2 then
begin
Skew := ANumCases * M3 / ((ANumCases - 1) * (ANumCases - 3) * stdDev3);
num := 6.0 * ANumCases * (ANumCases - 1);
denom := (ANumCases - 2) * (ANumCases + 1) * (ANumCases + 3);
StdErrorSkew := sqrt(num / denom);
end;
if ANumCases > 3 then
begin
num := ANumCases * (ANumCases + 1) * M4 - 3 * M2 * M2 * (ANumCases - 1);
denom := (ANumCases - 1) * (ANumCases - 2) * (ANumCases - 3) * stdDev4;
Kurtosis := num / denom;
num := 4.0 * (sqr(ANumCases) - 1) * sqr(StdErrorSkew);
denom := (ANumCases - 3) * (ANumCases + 5);
StdErrorKurtosis := sqrt(num / denom);
end;
end;
procedure TDescriptiveStats.Calc_Sum_SumOfSquares_Min_Max(const AValues: DblDyneVec;
out ASum, ASumOfSquares, AMin, AMax: Double);
var
i: Integer;
begin
ASum := 0.0;
ASumOfSquares := 0;
AMin := Infinity;
AMax := -Infinity;
for i := 0 to High(AValues) do
begin
ASum := ASum + AValues[i];
ASumOfSquares := ASumOfSquares + sqr(AValues[i]);
if AValues[i] < AMin then AMin := AValues[i];
if AValues[i] > AMax then AMax := AValues[i];
end;
end;
procedure TDescriptiveStats.CollectValues(out AValues: DblDyneVec);
var
i, n: Integer;
begin
AValues := nil; // silence the compiler
SetLength(AValues, NoCases);
n := 0;
for i := 1 to NoCases do
begin
if (doCasewiseDeletion in FOptions) then
begin
// Do not consider a case when any variable is empty
if not ValidValue(i, FColIndex) then
continue;
end else
begin
// Do not consider a case when the current variable is empty
if not GoodRecord(i, Length(FColsSelected), FColsSelected) then
continue;
end;
if TryStrToFloat(FDataGrid.Cells[FColIndex, i], AValues[n]) then
inc(n)
else
raise Exception.CreateFmt('Invalid number: variable "%s", case "%s"',
[FDataGrid.cells[FColIndex, 0], FDataGrid.Cells[0, i]]);
end;
SetLength(AValues, n);
end;
// Computes the percentile ranks of values stored in the data grid at the
// loaded columns. The values are assumed to be sorted.
procedure TDescriptiveStats.PercentileRank(const AValues: DblDyneVec; out
ACategoryValues, APercentiles: DblDyneVec; out AFreq: IntDyneVec);
var
i, nCases, iCat, nCategories: Integer;
lastCategoryValue: Double;
cumFreqCentered: Double;
cumFreq: Integer;
begin
// silence the compiler
ACategoryvalues := nil;
AFreq := nil;
APercentiles := nil;
nCases := Length(AValues);
SetLength(ACategoryValues, nCases); // over-dimension; will be trimmed later
SetLength(AFreq, nCases);
// Get count of unique values and frequencies of each
lastCategoryValue := AValues[0];
ACategoryValues[0] := lastCategoryValue;
AFreq[0] := 1;
iCat := 0;
for i := 1 to nCases-1 do
begin
if (lastCategoryValue = AValues[i]) then
AFreq[iCat] := AFreq[iCat] + 1
else
begin // new value
inc(iCat);
AFreq[iCat] := 1;
lastCategoryValue := AValues[i];
ACategoryValues[iCat] := lastCategoryValue;
end;
end;
// trim arrays
nCategories := iCat + 1;
SetLength(ACategoryValues, nCategories);
SetLength(AFreq, nCategories);
// Get cumulative frequencies and percentile ranks
SetLength(APercentiles, nCategories);
APercentiles[0] := AFreq[0] * 0.5 / nCases;
cumFreq := AFreq[0];
for i := 1 to nCategories-1 do // NOTE: This loop must begin at index 1
begin
cumFreqCentered := cumFreq + AFreq[i]*0.5; // cum frequencies at mid-point
APercentiles[i] := cumFreqCentered / nCases;
cumFreq := cumFreq + AFreq[i];
end;
end;
procedure TDescriptiveStats.WriteToReport(AVarName: String; ADecPlaces: Integer;
AReport: TStrings);
var
w: Integer;
nCategories: Integer;
i: Integer;
cumFreq: Integer;
m: TQuartileMethod;
begin
w := 10 + ADecPlaces - 3;
AReport.Add('VARIABLE: %*s', [W, '"' + AVarName + '"']);
AReport.Add('');
AReport.Add('Number of cases: %*d', [W, FNumCases]);
AReport.Add('Sum: %*.*f', [W, ADecPlaces, FSum]);
AReport.Add('Mean: %*.*f', [W, ADecPlaces, FMean]);
AReport.Add('Variance: %*.*f', [W, ADecPlaces, FVariance]);
AReport.Add('Std.Dev.: %*.*f', [W, ADecPlaces, FStdDev]);
AReport.Add('Std.Error of Mean %*.*f', [W, ADecPlaces, FStdErrorMean]);
AReport.Add('%.2f%% Conf.Interval Mean: %.*f to %.*f', [
FConfLevel*100.0, ADecPlaces, FMean - FDeltaMean, ADecPlaces, FMean + FDeltaMean]);
AReport.Add('');
AReport.Add('Minimum: %*.*f', [W, ADecPlaces, FMin]);
AReport.Add('Maximum: %*.*f', [W, ADecPlaces, FMax]);
AReport.Add('Range: %*.*f', [W, ADecPlaces, FMax - FMin]);
AReport.Add('');
AReport.Add('Skewness: %*.*f', [W, ADecPlaces, FSkew]);
AReport.Add('Std.Error of Skew: %*.*f', [W, ADecPlaces, FStdErrorSkew]);
AReport.Add('Kurtosis: %*.*f', [W, ADecPlaces, FKurtosis]);
AReport.Add('Std. Error of Kurtosis: %*.*f', [W, ADecPlaces, FStdErrorKurtosis]);
AReport.Add('');
AReport.Add('First Quartile: %*.*f', [W, ADecPlaces, FFirstQuartile]);
AReport.Add('Median: %*.*f', [W, ADecPlaces, FMedian]);
AReport.Add('Third Quartile: %*.*f', [W, ADecPlaces, FThirdQuartile]);
AReport.Add('Interquartile range: %*.*f', [W, ADecPlaces, FThirdQuartile - FFirstQuartile]);
if (doAlternativeQuartiles in FOptions) then
begin
AReport.Add('');
AReport.Add('');
AReport.Add('ALTERNATIVE METHODS FOR OBTAINING QUARTILES');
AReport.Add('');
AReport.Add('Method First Quartile Median Third Quartile');
AReport.Add('------ -------------- ---------- --------------');
for m := Low(TQuartileMethod) to High(TQuartileMethod) do
AReport.Add(' %d %12.3f %12.3f %12.3f', [m, FQuartiles[m, 1], FQuartiles[m, 2], FQuartiles[m, 3]]);
AReport.Add('');
AReport.Add('NOTES:');
AReport.Add('Method 1 is the weighted average at X[np] where ');
AReport.Add(' n is no. of cases, p is percentile / 100');
AReport.Add('Method 2 is the weighted average at X[(n+1)p] This is used in this program.');
AReport.Add('Method 3 is the empirical distribution function.');
AReport.Add('Method 4 is called the empirical distribution function - averaging.');
AReport.Add('Method 5 is called the empirical distribution function = Interpolation.');
AReport.Add('Method 6 is the closest observation method.');
AReport.Add('Method 7 is from the TrueBasic Statistics Graphics Toolkit.');
AReport.Add('Method 8 was used in an older Microsoft Excel version.');
AReport.Add('See the internet site http://www.xycoon.com/ for the above.');
end;
if (doPercentileRanks in FOptions) then
begin
nCategories := Length(FCategoryValues);
cumFreq := 0;
AReport.Add('');
AReport.Add('');
AReport.Add('PERCENTILE RANKS');
AReport.Add('');
AReport.Add('Score Value Frequency Cum.Freq. Percentile Rank');
AReport.Add('----------- --------- --------- ---------------');
for i := 0 to nCategories-1 do
begin
cumFreq := cumFreq + FFreqValues[i];
AReport.Add(' %8.3f %8d %8d %12.2f%%', [
FCategoryValues[i], FFreqValues[i], cumFreq, FPercentiles[i]*100.0
]);
end;
end;
end;
{ TDescriptiveFrm } { TDescriptiveFrm }
constructor TDescriptiveFrm.Create(AOwner: TComponent);
begin
inherited;
FReportFrame.Parent := ReportPage;
FReportFrame.BorderSpacing.Left := 0;
FReportFrame.BorderSpacing.Top := 0;
FReportFrame.BorderSpacing.Bottom := 0;
FReportFrame.BorderSpacing.Right := 0;
end;
procedure TDescriptiveFrm.AdjustConstraints; procedure TDescriptiveFrm.AdjustConstraints;
begin begin
ParamsPanel.Constraints.MinHeight := AllBtn.Top + AllBtn.Height + OptionsGroup.Height + ParamsPanel.Constraints.MinHeight := AllBtn.Top + AllBtn.Height + OptionsGroup.Height +
CIEdit.Height + ButtonBevel.Height + CloseBtn.Height + VarList.BorderSpacing.Bottom + CIEdit.Height + ButtonBevel.Height + CloseBtn.Height + VarList.BorderSpacing.Bottom +
OptionsGroup.BorderSpacing.Bottom + CloseBtn.BorderSpacing.Top; OptionsGroup.BorderSpacing.Bottom + CloseBtn.BorderSpacing.Top +
DecPlacesEdit.Height + DecPlacesEdit.BorderSpacing.Top;
ParamsPanel.Constraints.MinWidth := Math.Max( ParamsPanel.Constraints.MinWidth := Math.Max(
4*CloseBtn.Width + 3*HelpBtn.BorderSpacing.Right, 4*CloseBtn.Width + 3*HelpBtn.BorderSpacing.Right,
OptionsGroup.Width OptionsGroup.Width
@ -90,275 +507,100 @@ end;
procedure TDescriptiveFrm.Compute; procedure TDescriptiveFrm.Compute;
var var
i, j, k, m: integer;
nCases, noSelected: integer;
Q1, Q2, Q3, Q12, Q13, Q14, Q15, Q16, Q17, Q18, Q22, Q23, Q24, Q25, Q26: double;
Q27, Q28, Q32, Q33, Q34, Q35, Q36, Q37, Q38, IQrange: double;
num, den, cases: double;
values: DblDyneVec = nil;
pcntRank: DblDyneVec = nil;
selected: IntDyneVec = nil;
cellString: String; cellString: String;
i, j: Integer;
noSelected: Integer;
selected: IntDyneVec = nil;
page: TTabSheet;
reportFrame: TReportFrame;
lReport: TStrings; lReport: TStrings;
lDescrStats: TDescriptiveStats;
options: TDescriptiveOptions;
begin begin
NoSelected := SelList.Items.Count; noSelected := SelList.Items.Count;
if noSelected = 0 then if noSelected = 0 then
begin begin
MessageDlg('No variables selected.', mtError, [mbOK], 0); MessageDlg('No variables selected.', mtError, [mbOK], 0);
exit; exit;
end; end;
SetLength(selected, noSelected); SetLength(selected, noSelected);
// Get selected variables // Find column index of selected variables
for i := 1 to noselected do for i := 0 to noSelected - 1 do
begin begin
cellstring := SelList.Items.Strings[i-1]; cellstring := SelList.Items[i];
for j := 1 to NoVariables do for j := 1 to NoVariables do
if cellstring = OS3MainFrm.DataGrid.Cells[j,0] then selected[i-1] := j; if cellstring = OS3MainFrm.DataGrid.Cells[j,0] then selected[i] := j;
end; end;
lReport := TStringList.Create; // Create a tabsheet with ReportFrame for each selected variable (in addition to the built-in one)
try if noSelected > PageControl.PageCount then
lReport.Add('DISTRIBUTION PARAMETER ESTIMATES'); begin
lReport.Add(''); for i := 1 to noSelected-1 do // we do not create a tab for the first variable - it exists by default
SetLength(Values, NoCases);
SetLength(pcntRank, NoCases);
for j := 1 to noSelected do
begin begin
deviation := 0.0; page := TTabSheet.Create(PageControl);
devsqr := 0.0; page.Parent := PageControl;
M2 := 0.0; reportFrame := TReportFrame.Create(page);
M3 := 0.0; reportFrame.Parent := page;
M4 := 0.0; reportFrame.Align := alClient;
sum := 0.0; InitToolBar(reportFrame.ReportToolbar, tpRight);
variance := 0.0; end;
stddev := 0.0; end;
range := 0.0;
skew := 0.0;
kurtosis := 0.0;
ncases := 0;
df := 0.0;
seskew := 0.0;
kurtosis := 0.0;
sekurtosis := 0.0;
k := selected[j-1];
CI := StrToFloat(CIEdit.Text) / 100.0;
prob := CI;
CI := (1.0 - CI) / 2.0;
CI := 1.0 - CI;
if ZScoresToGridChk.Checked then // add a new column to the grid // Remove excess pages from previous session
begin while PageControl.PageCount > noSelected do
cellstring := OS3MainFrm.DataGrid.Cells[k,0] + 'z'; PageControl.Pages[PageControl.PageCount-1].Free;
DictionaryFrm.NewVar(NoVariables + 1);
DictionaryFrm.DictGrid.Cells[1, NoVariables] := cellstring;
OS3MainFrm.DataGrid.Cells[NoVariables, 0] := cellstring;
end;
// Accumulate sums of squares, sums, etc. for variable j // Every tab gets the name of the corresponding variable.
min := 1.0e308; for i := 0 to NoSelected-1 do
max := -1.0e308; PageControl.Pages[i].Caption := OS3MainFrm.DataGrid.Cells[selected[i], 0];
for i := 1 to NoCases do
begin
if not GoodRecord(i, noSelected, selected) then
continue;
if CaseChk.Checked then // Prepare options
begin options := [];
if not ValidValue(i, selected[j-1]) then if PercentileChk.Checked then Include(options, doPercentileRanks);
continue; if AllQuartilesChk.Checked then Include(options, doAlternativeQuartiles);
end if CaseChk.Checked then Include(options, doCasewiseDeletion);
else if not GoodRecord(i, noselected, selected) then
continue;
value := StrToFloat(OS3MainFrm.DataGrid.Cells[k,i]); lReport := TStringList.Create;
ncases := ncases + 1; lDescrStats := TDescriptiveStats.Create(OS3MainFrm.DataGrid, selected, StrToFloat(CIEdit.Text)/100);
values[ncases-1] := value; try
df := df + 1.0; for i := 0 to noSelected-1 do
sum := sum + value; begin
variance := variance + (value * value); // Analyze the data and get descriptive stats
if (value < min) then min := value; lDescrStats.Analyze(selected[i], options);
if (value > max) then max := value;
end;
if ncases > 0 then // Store z values, (value - mean) / stdDev, to grid, if needed
begin zScoresToGrid(selected[i], selected, lDescrStats.Mean, lDescrStats.StdDev);
mean := sum / ncases;
range := max - min;
end;
if ncases > 1 then // Write descriptive stats to report
begin lReport.Clear;
variance := variance - (sum * sum) / ncases; lReport.Add('DISTRIBUTION PARAMETER ESTIMATES');
variance := variance / (ncases - 1);
stddev := sqrt(variance);
semean := sqrt(variance / ncases);
if ncases < 120 then
CI := semean * inverset(CI,df)
else
CI := semean * inversez(CI);
end;
if variance = 0.0 then
begin
cellstring := OS3MainFrm.DataGrid.Cells[k,0];
MessageDlg('No Variability in '+ cellstring + ' variable - ending analysis.', mtInformation, [mbOK], 0);
exit;
end;
if ncases > 3 then // obtain skew, kurtosis and z scores
begin
for i := 1 to NoCases do
begin
if CaseChk.Checked then
begin
if not ValidValue(i, selected[j-1]) then continue;
end else
if not GoodRecord(i, noselected, selected) then continue;
value := StrToFloat(OS3MainFrm.DataGrid.Cells[k,i]);
if stddev > 0.0 then
begin
deviation := value - mean;
devsqr := deviation * deviation;
M2 := M2 + devsqr;
M3 := M3 + (deviation * devsqr);
M4 := M4 + (devsqr * devsqr);
z := (value - mean) / stddev;
if ZScoresToGridChk.Checked then
begin
cellstring := format('%8.5f',[z]);
OS3MainFrm.DataGrid.Cells[NoVariables,i] := cellstring;
end;
end;
end;
if ncases > 2 then
begin
skew := (ncases * M3) / ((ncases - 1) * (ncases - 2) * stddev * variance);
cases := ncases;
num := 6.0 * cases * (cases - 1.0);
den := (cases - 2.0) * (cases + 1.0) * (cases + 3.0);
seskew := sqrt(num / den);
end;
if ncases > 3 then
begin
kurtosis := (ncases * (ncases + 1) * M4) - (3 * M2 * M2 * (ncases - 1));
kurtosis := kurtosis / ( (ncases - 1) * (ncases - 2) * (ncases - 3) * (variance * variance) );
sekurtosis := sqrt((4.0 * (ncases * ncases - 1) * (seskew * seskew)) / ((ncases - 3) * (ncases + 5)));
end;
end;
// output results for the kth variable
cellstring := OS3MainFrm.DataGrid.Cells[k,0];
if j > 1 then lReport.Add('');
lReport.Add('VARIABLE: %10s', ['"' + cellString + '"']);
lReport.Add('');
lReport.Add('Number of cases: %10d', [nCases]);
lReport.Add('Sum: %10.3f', [sum]);
lReport.Add('Mean: %10.3f', [mean]);
lReport.Add('Variance: %10.3f', [variance]);
lReport.Add('Std.Dev.: %10.3f', [stddev]);
lReport.Add('Std.Error of Mean %10.3f', [seMean]);
lReport.Add('%.2f%% Conf.Interval Mean: %10.3f to %.3f', [prob*100.0, mean - CI, mean + CI]);
lReport.Add('Range: %10.3f', [range]);
lReport.Add('Minimum: %10.3f', [min]);
lReport.Add('Maximum: %10.3f', [max]);
lReport.Add('Skewness: %10.3f', [skew]);
lReport.Add('Std.Error of Skew: %10.3f', [seSkew]);
lReport.Add('Kurtosis: %10.3f', [kurtosis]);
lReport.Add('Std. Error of Kurtosis: %10.3f', [seKurtosis]);
lReport.Add(''); lReport.Add('');
lDescrStats.WriteToReport(trim(OS3MainFrm.DataGrid.Cells[selected[i], 0]),
DecPlacesEdit.Value, lReport);
if ncases > 4 then // get percentiles and quartiles // Display report in the page of the variable
begin reportFrame := GetReportFrame(i);
// get percentile ranks reportFrame.DisplayReport(lReport);
if pcntileChk.Checked then PRank(k, pcntRank, lReport); end;
// sort values and get quartiles
for i := 0 to ncases - 2 do
begin
for m := i + 1 to ncases -1 do
begin
if values[i] > values[m] then
begin
value := values[i];
values[i] := values[m];
values[m] := value;
end;
end;
end;
Q1 := Quartiles(2,0.25,ncases,values);
Q2 := Quartiles(2,0.5,ncases,values);
Q3 := Quartiles(2,0.75,ncases,values);
IQrange := Q3 - Q1;
lReport.Add('First Quartile: %10.3f', [Q1]);
lReport.Add('Median: %10.3f', [Q2]);
lReport.Add('Third Quartile: %10.3f', [Q3]);
lReport.Add('Interquartile range: %10.3f', [IQrange]);
lReport.Add('');
end;
if (AllQrtilesChk.Checked) then
begin
lReport.Add('Alternative Methods for Obtaining Quartiles');
lReport.Add(' Method 1 2 3 4 5 6 7 8');
lReport.Add('Pcntile');
Q1 := Quartiles(1,0.25,ncases,values);
Q12 := Quartiles(2,0.25,ncases,values);
Q13 := Quartiles(3,0.25,ncases,values);
Q14 := Quartiles(4,0.25,ncases,values);
Q15 := Quartiles(5,0.25,ncases,values);
Q16 := Quartiles(6,0.25,ncases,values);
Q17 := Quartiles(7,0.25,ncases,values);
Q18 := Quartiles(8,0.25,ncases,values);
lReport.Add('Q1 %8.3f%8.3f%8.3f%8.3f%8.3f%8.3f%8.3f%8.3f', [Q1,Q12,Q13,Q14,Q15,Q16,Q17,Q18]);
Q2 := Quartiles(1,0.5,ncases,values);
Q22 := Quartiles(2,0.5,ncases,values);
Q23 := Quartiles(3,0.5,ncases,values);
Q24 := Quartiles(4,0.5,ncases,values);
Q25 := Quartiles(5,0.5,ncases,values);
Q26 := Quartiles(6,0.5,ncases,values);
Q27 := Quartiles(7,0.5,ncases,values);
Q28 := Quartiles(8,0.5,ncases,values);
lReport.Add('Q2 %8.3f%8.3f%8.3f%8.3f%8.3f%8.3f%8.3f%8.3f', [Q2,Q22,Q23,Q24,Q25,Q26,Q27,Q28]);
Q3 := Quartiles(1,0.75,ncases,values);
Q32 := Quartiles(2,0.75,ncases,values);
Q33 := Quartiles(3,0.75,ncases,values);
Q34 := Quartiles(4,0.75,ncases,values);
Q35 := Quartiles(5,0.75,ncases,values);
Q36 := Quartiles(6,0.75,ncases,values);
Q37 := Quartiles(7,0.75,ncases,values);
Q38 := Quartiles(8,0.75,ncases,values);
lReport.Add('Q3 %8.3f%8.3f%8.3f%8.3f%8.3f%8.3f%8.3f%8.3f', [Q3,Q32,Q33,Q34,Q35,Q36,Q37,Q38]);
lReport.Add('');
lReport.Add('NOTES:');
lReport.Add('Method 1 is the weighted average at X[np] where ');
lReport.Add(' n is no. of cases, p is percentile / 100');
lReport.Add('Method 2 is the weighted average at X[(n+1)p] This is used in this program.');
lReport.Add('Method 3 is the empirical distribution function.');
lReport.Add('Method 4 is called the empirical distribution function - averaging.');
lReport.Add('Method 5 is called the empirical distribution function = Interpolation.');
lReport.Add('Method 6 is the closest observation method.');
lReport.Add('Method 7 is from the TrueBasic Statistics Graphics Toolkit.');
lReport.Add('Method 8 was used in an older Microsoft Excel version.');
lReport.Add('See the internet site http://www.xycoon.com/ for the above.');
lReport.Add('');
end; // end of experimental alternatives
lReport.Add(DIVIDER_SMALL_AUTO);
end; // next j variable
FReportFrame.DisplayReport(lReport);
finally finally
// Clean up
lDescrStats.Free;
lReport.Free; lReport.Free;
Selected := nil; end;
Values := nil; end;
pcntrank := nil;
function TDescriptiveFrm.GetReportFrame(APageIndex: Integer): TReportFrame;
var
page: TTabSheet;
begin
Result := nil;
if (APageIndex >=0) and (APageIndex < PageControl.PageCount) then
begin
page := PageControl.Pages[APageIndex];
if (page.ControlCount > 0) and (page.Controls[0] is TReportFrame) then
Result := TReportFrame(page.Controls[0]);
end; end;
end; end;
@ -406,6 +648,12 @@ var
i: integer; i: integer;
begin begin
inherited; inherited;
for i := PageControl.PageCount-1 downto 1 do
PageControl.Pages[i].Free;
PageControl.Pages[0].Caption := 'Report';
CIEdit.Text := FormatFloat('0.0', DEFAULT_CONFIDENCE_LEVEL_PERCENT); CIEdit.Text := FormatFloat('0.0', DEFAULT_CONFIDENCE_LEVEL_PERCENT);
VarList.Clear; VarList.Clear;
SelList.Clear; SelList.Clear;
@ -447,9 +695,16 @@ procedure TDescriptiveFrm.UpdateBtnStates;
var var
lSelected: Boolean; lSelected: Boolean;
i: Integer; i: Integer;
F: TReportFrame;
begin begin
inherited; inherited;
for i := 0 to PageControl.PageCount-1 do
begin
F := GetReportFrame(i);
if Assigned(F) then F.Clear;
end;
lSelected := false; lSelected := false;
for i := 0 to VarList.Items.Count-1 do for i := 0 to VarList.Items.Count-1 do
if VarList.Selected[i] then if VarList.Selected[i] then
@ -478,5 +733,43 @@ begin
end; end;
procedure TDescriptiveFrm.zScoresToGrid(AColIndex: Integer;
const AColsSelected: IntDyneVec; AMean, AStdDev: Double);
var
i, idx: Integer;
value, zValue: Double;
varName: String;
begin
if AStdDev = 0 then begin
ErrorMsg('Cannot store z values to grid because StdDev is zero.');
exit;
end;
varName := OS3MainFrm.DataGrid.Cells[AColIndex, 0] + '_z';
idx := OS3MainFrm.DataGrid.Rows[0].IndexOf(varName);
if idx = -1 then
begin
DictionaryFrm.NewVar(NoVariables + 1);
DictionaryFrm.DictGrid.Cells[1, NoVariables] := varName;
OS3MainFrm.DataGrid.Cells[NoVariables, 0] := varName;
idx := NoVariables;
end;
for i := 1 to NoCases do
begin
if CaseChk.Checked then
begin
if not ValidValue(i, AColsSelected[AColIndex]) then continue;
end
else
if not GoodRecord(i, Length(AColsSelected), AColsSelected) then continue;
value := StrToFloat(OS3MainFrm.DataGrid.Cells[AColIndex, i]);
zValue := (value - AMean) / AStdDev;
OS3MainFrm.DataGrid.Cells[idx, i] := Format('%8.5f', [zValue]);
// to do: read number of decimal places from Dictionary and use in Format().
end;
end;
end. end.

2
applications/lazstats/source/forms/misc/basicstatsparamsformunit.lfm
View File

@ -1,6 +1,8 @@
inherited BasicStatsParamsForm: TBasicStatsParamsForm inherited BasicStatsParamsForm: TBasicStatsParamsForm
Height = 459
Width = 709 Width = 709
Caption = 'BasicStatsParamsForm' Caption = 'BasicStatsParamsForm'
ClientHeight = 459
ClientWidth = 709 ClientWidth = 709
Position = poMainFormCenter Position = poMainFormCenter
object ParamsPanel: TPanel[0] object ParamsPanel: TPanel[0]

4
applications/lazstats/source/forms/misc/basicstatsparamsformunit.pas
View File

@ -77,7 +77,7 @@ begin
exit; exit;
w := MaxValue([HelpBtn.Width, ResetBtn.Width, ComputeBtn.Width, CloseBtn.Width]); w := MaxValue([HelpBtn.Width, ResetBtn.Width, ComputeBtn.Width, CloseBtn.Width]);
HelpBtn.Constraints.MinWidth := 2; HelpBtn.Constraints.MinWidth := w;
ResetBtn.Constraints.MinWidth := w; ResetBtn.Constraints.MinWidth := w;
ComputeBtn.Constraints.MinWidth := w; ComputeBtn.Constraints.MinWidth := w;
CloseBtn.Constraints.MinWidth := w; CloseBtn.Constraints.MinWidth := w;
@ -89,6 +89,8 @@ begin
Position := poDesigned; Position := poDesigned;
FAutoSized := true; FAutoSized := true;
inherited;
end; end;

119
applications/lazstats/source/units/functionslib.pas
View File

@ -24,7 +24,7 @@ function poly(const c: Array of double; nord: integer; x: double): double; // RE
procedure swilk (var init : boolean; const x: DblDyneVec; n, n1, n2: integer; procedure swilk (var init : boolean; const x: DblDyneVec; n, n1, n2: integer;
const a: DblDyneVec; var w, pw: double; out ifault: integer); const a: DblDyneVec; var w, pw: double; out ifault: integer);
procedure SVDinverse(VAR a : DblDyneMat; N : integer); procedure SVDinverse(VAR a : DblDyneMat; N : integer);
function inverset(Probt, DF : double) : double; function InverseT(Prob, DF: double): double;
function inversechi(p : double; k : integer) : double; function inversechi(p : double; k : integer) : double;
function STUDENT(q,v,r : real) : real; function STUDENT(q,v,r : real) : real;
function realraise(base,power : double ): double; function realraise(base,power : double ): double;
@ -43,10 +43,12 @@ function UniStats(N : integer; VAR X : DblDyneVec; VAR z : DblDyneVec;
VAR SESkew : double; VAR SEkurtosis : double; VAR min : double; VAR SESkew : double; VAR SEkurtosis : double; VAR min : double;
VAR max : double; VAR Range : double; VAR MissValue : string) : VAR max : double; VAR Range : double; VAR MissValue : string) :
integer; integer;
function WholeValue(value : double) : double;
function FractionValue(value : double) : double; //function WholeValue(value : double) : double;
function Quartiles(TypeQ : integer; pcntile : double; N : integer; //function FractionValue(value : double) : double;
VAR values : DblDyneVec) : double;
function Quartiles(TypeQ: integer; Percentile: double; N: integer;
const Values: DblDyneVec): double;
function KolmogorovProb(z: double): double; function KolmogorovProb(z: double): double;
function KolmogorovTest(na: integer; const a: DblDyneVec; nb: integer; function KolmogorovTest(na: integer; const a: DblDyneVec; nb: integer;
@ -944,15 +946,14 @@ begin
Result := prob; Result := prob;
end; end;
function inverset(Probt, DF : double) : double; { Returns the t value corresponding to a two-tailed t test probability. }
function InverseT(Prob, DF: double): double;
var var
z, W, tValue: double; z, W: double;
begin begin
// Returns the t value corresponding to a two-tailed t test probability. z := InverseZ(Prob);
z := inversez(Probt); W := z * ((8.0 * DF + 3.0) / (1.0 + 8.0 * DF));
W := z * ((8.0 * DF + 3.0) / (1.0 + 8.0 * DF)); Result := sqrt(DF * (exp(W * W / DF) - 1.0));
tValue := sqrt(DF * (exp(W * W / DF) - 1.0));
inverset := tValue;
end; end;
//--------------------------------------------------------------------- //---------------------------------------------------------------------
@ -1644,11 +1645,11 @@ begin
end; end;
function Quartiles(TypeQ : integer; pcntile : double; N : integer; function Quartiles(TypeQ: integer; Percentile: double; N: integer;
VAR values : DblDyneVec) : double; const Values: DblDyneVec): double;
VAR var
whole, fraction, Myresult, np, avalue, avalue1 : double; whole, fraction, np, lValue, lValue1: double;
subscript : integer; subscript: integer;
begin begin
{ for i := 0 to N - 1 do // this is for debugging { for i := 0 to N - 1 do // this is for debugging
begin begin
@ -1656,46 +1657,52 @@ begin
OutPutFrm.RichEdit.Lines.Add(outline); OutPutFrm.RichEdit.Lines.Add(outline);
end; end;
OutPutFrm.ShowModal; OutPutFrm.ShowModal;
OutPutFrm.RichEdit.Clear; } OutPutFrm.RichEdit.Clear;
case TypeQ of }
1 : np := pcntile * N; case TypeQ of
2 : np := pcntile * (N + 1); 1 : np := Percentile * N;
3 : np := pcntile * N; 2 : np := Percentile * (N + 1);
4 : np := pcntile * N; 3 : np := Percentile * N;
5 : np := pcntile * (N - 1); 4 : np := Percentile * N;
6 : np := pcntile * N + 0.5; 5 : np := Percentile * (N - 1);
7 : np := pcntile * (N + 1); 6 : np := Percentile * N + 0.5;
8 : np := pcntile * (N + 1); 7 : np := Percentile * (N + 1);
8 : np := Percentile * (N + 1);
end;
whole := WholeValue(np);
fraction := FractionValue(np);
subscript := Trunc(whole) - 1;
lValue := Values[subscript];
lValue1 := Values[subscript + 1];
case TypeQ of
1 : Result := ((1.0 - fraction) * values[subscript]) + fraction * values[subscript + 1];
2 : Result := ((1.0 - fraction) * lValue) + fraction * lValue1; // values[subscript + 1];
3 : if (fraction = 0.0) then
Result := values[subscript]
else
Result := values[subscript + 1];
4 : if (fraction = 0.0) then
Result := 0.5 * (values[subscript] + values[subscript + 1])
else
Result := values[subscript + 1];
5 : if (fraction = 0.0) then
Result := values[subscript + 1]
else
Result := Values[subscript + 1] + fraction * (Values[subscript + 2] - values[subscript + 1]);
6 : Result := values[subscript];
7 : if (fraction = 0.0) then
Result := values[subscript]
else
Result := fraction * Values[subscript] + (1.0 - fraction) * Values[subscript + 1];
8 : begin
if (fraction = 0.0) then Result := values[subscript];
if (fraction = 0.5) then Result := 0.5 * (values[subscript] + values[subscript + 1]);
if (fraction < 0.5) then Result := values[subscript];
if (fraction > 0.5) then Result := values[subscript + 1];
end; end;
whole := WholeValue(np); end;
fraction := FractionValue(np);
subscript := Trunc(whole) - 1;
avalue := values[subscript];
avalue1 := values[subscript + 1];
case TypeQ of
1 : Myresult := ((1.0 - fraction) * values[subscript]) +
fraction * values[subscript + 1];
2 : Myresult := ((1.0 - fraction) * avalue) +
fraction * avalue1; // values[subscript + 1];
3 : if (fraction = 0.0) then Myresult := values[subscript]
else Myresult := values[subscript + 1];
4 : if (fraction = 0.0) then Myresult := 0.5 * (values[subscript] + values[subscript + 1])
else Myresult := values[subscript + 1];
5 : if (fraction = 0.0) then Myresult := values[subscript + 1]
else Myresult := values[subscript + 1] + fraction * (values[subscript + 2] -
values[subscript + 1]);
6 : Myresult := values[subscript];
7 : if (fraction = 0.0) then Myresult := values[subscript]
else Myresult := fraction * values[subscript] +
(1.0 - fraction) * values[subscript + 1];
8 : begin
if (fraction = 0.0) then Myresult := values[subscript];
if (fraction = 0.5) then Myresult := 0.5 * (values[subscript] + values[subscript + 1]);
if (fraction < 0.5) then Myresult := values[subscript];
if (fraction > 0.5) then Myresult := values[subscript + 1];
end;
end;
Result := Myresult;
end; end;
function KolmogorovProb(z : double) : double; function KolmogorovProb(z : double) : double;