Bell Curve on basic charts

AFL Programming
1

Dear Forun,

I am trying to put in a bell curve on a basic line graph that tracks the variation from the 200 DMA. The very basic code

_SECTION_BEGIN("200 DMA var");

DEMA200 = EMA(C,200);
DMA200VarPer = ((C-DEMA200)/DEMA200)*100;
Plot(DMA200VarPer,"DMA200Var",colorRed,styleLine);
Plot(0,"Zero",colorBlack,styleLine|styleDashed);

Filter =1;
AddColumn(C,"Close",1.2);
AddColumn(DEMA200,"DEMA200",1.2);
AddColumn(DMA200VarPer,"DEMA200Var",1.2);

_SECTION_END();

Wish to have a bell curve (normal distribution with probability) plotted on the 2nd pane with red line chart. How do we visualise it?

Request guidance on whether to use - Visual Range or Predefine Range for bars.

2 
// Bell Curve: Close Price vs 200-Day MA Distribution
// Plots histogram + Gaussian fit for (Close / MA200) ratios

// Parameters
MA_Period = 200;
Num_Bins = 50; // Adjust for smoother histogram
Min_Ratio = 0.5; // X-axis range
Max_Ratio = 1.5;
Bin_Width = (Max_Ratio - Min_Ratio) / Num_Bins;

// Compute ratios (only where MA is valid)
MA200 = MA(Close, MA_Period);
Ratio = IIf(MA200 > 0, Close / MA200, Null); // Avoid div by zero
Valid_Ratio = IIf(BarIndex() >= MA_Period - 1 AND !IsNull(Ratio), Ratio, Null);

// Collect valid ratios into an array
Num_Bars = BarCount;
Ratio_Array = Null;
for(i = MA_Period - 1; i < Num_Bars; i++) {
    if(!IsNull(Valid_Ratio[i])) {
        Ratio_Array[i] = Valid_Ratio[i];
    }
}

// Compute histogram
Hist = 0;
for(i = MA_Period - 1; i < Num_Bars; i++) {
    if(!IsNull(Ratio_Array[i])) {
        bin_idx = Floor((Ratio_Array[i] - Min_Ratio) / Bin_Width);
        if(bin_idx >= 0 AND bin_idx < Num_Bins) {
            Hist[bin_idx] = Nz(Hist[bin_idx]) + 1;
        }
    }
}

// Compute Gaussian parameters (mean and std dev)
Sum_R = 0; Count = 0; Sum_Sq = 0;
for(i = MA_Period - 1; i < Num_Bars; i++) {
    r = Ratio_Array[i];
    if(!IsNull(r)) {
        Sum_R += r;
        Sum_Sq += r * r;
        Count++;
    }
}
Mean = IIf(Count > 0, Sum_R / Count, 0);
Variance = IIf(Count > 0, (Sum_Sq / Count) - (Mean * Mean), 0);
StdDev = IIf(Count > 0, sqrt(Max(Variance, 0)), 0);

// Normalize histogram
Max_Hist = 0;
for(i = 0; i < Num_Bins; i++) {
    if(Nz(Hist[i]) > Max_Hist) Max_Hist = Nz(Hist[i]);
}
Norm_Hist = IIf(Max_Hist > 0, Hist / Max_Hist, 0);

// Gaussian curve points
GraphX = 0; GraphY = 0; Max_GraphY = 0;
for(i = 0; i < Num_Bins; i++) {
    x = Min_Ratio + (i + 0.5) * Bin_Width;
    GraphX[i] = x;
    if(StdDev > 0.0001) { // Added small threshold to prevent div by zero
        GraphY[i] = exp(-((x - Mean) / (2 * StdDev * StdDev)) ^ 2) / (StdDev * sqrt(2 * 3.14159));
    } else {
        GraphY[i] = 0;
    }
    if(GraphY[i] > Max_GraphY) Max_GraphY = GraphY[i];
}
GraphY = IIf(Max_GraphY > 0, GraphY * Max_Hist / Max_GraphY, 0);

// Plot main chart
Plot(Close, "Close", colorBlack, styleCandle);
Plot(MA200, "200 DMA", colorBlue, styleLine);

// Custom pane for bell curve
_SECTION_BEGIN("Bell Curve");
SetChartOptions(0, chartShowArrows | chartShowDates);
SetChartBkColor(colorWhite);

// Gfx setup
Pane_Width = Status("pxwidth") / 2; // Dynamic scaling
Pane_Height = 100;
GfxSetOverlayMode(1);
GfxSelectFont("Arial", 10);
GfxSetBkMode(1);

// Draw axes
GfxSelectPen(colorRGB(128,128,128), 1);
GfxMoveTo(10, Pane_Height - 10); GfxLineTo(Pane_Width - 10, Pane_Height - 10); // X axis
GfxMoveTo(10, 10); GfxLineTo(10, Pane_Height - 10); // Y axis

// Labels
GfxTextOut("Ratio (Close / 200DMA)", Pane_Width / 2 - 50, Pane_Height - 5);
GfxTextOut("Frequency", 5, Pane_Height / 2);

// Draw histogram bars
GfxSelectSolidBrush(colorRGB(135,206,250)); // Light blue
for(i = 0; i < Num_Bins; i++) {
    bar_height = (Pane_Height - 20) * Nz(Norm_Hist[i]);
    bar_x = 10 + (i * ((Pane_Width - 20) / Num_Bins));
    GfxRectangle(bar_x, Pane_Height - 10 - bar_height, bar_x + ((Pane_Width - 20) / Num_Bins) - 2, Pane_Height - 10);
}

// Draw Gaussian curve
GfxSelectPen(colorRed, 2);
first_point = True;
for(i = 0; i < Num_Bins; i++) {
    curve_y = 10 + (Pane_Height - 20) * Nz(GraphY[i] / Max_Hist);
    curve_x = 10 + (i * ((Pane_Width - 20) / Num_Bins));
    if(first_point) {
        GfxMoveTo(curve_x, Pane_Height - 10 - curve_y);
        first_point = False;
    } else {
        GfxLineTo(curve_x, Pane_Height - 10 - curve_y);
    }
}

// Mean line
if(Count > 0) {
    GfxSelectPen(colorGreen, 1, 2); // Dashed
    GfxSetCoordsMode(1);
    x_scaled = 10 + ((Mean - Min_Ratio) / (Max_Ratio - Min_Ratio)) * (Pane_Width - 20);
    GfxMoveTo(x_scaled, 0);
    GfxLineTo(x_scaled, Pane_Height);
}

// Text annotations
GfxTextOut("Mean: " + NumToStr(Mean, 1.3), 10, 5);
GfxTextOut("StdDev: " + NumToStr(StdDev, 1.3), 10, 20);
GfxTextOut("Data Points: " + NumToStr(Count, 1.0), 10, 35);
_SECTION_END();

// Title
Title = StrFormat("{{NAME}} - {{INTERVAL}} {{DATE}} O=%.2f H=%.2f L=%.2f C=%.2f (%.1f%%) " +
                  "Ratio Mean=%.3f Std=%.3f",
                  O, H, L, C, SelectedValue(ROC(Close, 1)), Mean, StdDev);
4 Likes
3

@Anthony many thanks. That indeed is the bell curve. A bit simplistic approach I found through the inbuilt Gemini help is as follows:

_SECTION_BEGIN("200 DMA var");

LookbackPeriod = Param("Lookback for Stats", 252, 10, 500, 1); // e.g., 252 for a year of daily data
MAPeriod = Param("Moving Averages", 200, 10, 500, 1); // e.g., Moving Average of daily data

DEMA200 = EMA(C,MAPeriod);
DMA200VarPer = ((C-DEMA200)/DEMA200)*100;
Plot(DMA200VarPer,"DMA200Var",colorRed,styleLine|styleThick);
Plot(0,"Zero",colorBlack,styleLine);
// Bell Curve related plots (Mean and Standard Deviation lines)


MeanDMA200Var = MA(DMA200VarPer, LookbackPeriod);
StDevDMA200Var = StDev(DMA200VarPer, LookbackPeriod);

Plot(MeanDMA200Var, "Mean DMA200Var", colorViolet, styleLine);
Plot(MeanDMA200Var + StDevDMA200Var, "+1 StdDev", colorBlue, styleLine | styleDashed);
Plot(MeanDMA200Var - StDevDMA200Var, "-1 StdDev", colorBlue, styleLine | styleDashed);
Plot(MeanDMA200Var + 2 * StDevDMA200Var, "+2 StdDev", colorGreen, styleLine | styleDashed);
Plot(MeanDMA200Var - 2 * StDevDMA200Var, "-2 StdDev", colorGreen, styleLine | styleDashed);
Plot(MeanDMA200Var + 3 * StDevDMA200Var, "+3 StdDev", colorRed, styleLine | styleDashed);
Plot(MeanDMA200Var - 3 * StDevDMA200Var, "-3 StdDev", colorRed, styleLine | styleDashed);

Filter =1;
AddColumn(C,"Close",1.2);
AddColumn(DEMA200,"DEMA200",1.2);
AddColumn(DMA200VarPer,"DEMA200Var",1.2);

_SECTION_END();

Still thinking a bit, whether there should be a lookback or LAG inserted in there to understand where we stand as per historical data?

4

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