**Binary entropy function** is a mathematical concept that is used to measure the uncertainty or randomness of a binary system. In a binary system, there are only two possible outcomes, such as heads or tails in a coin toss. The binary entropy function is used to measure the probability of these two outcomes occurring.

In trading, the binary entropy function can be used to analyze the likelihood of a particular event occurring. For example, it can be used to analyze the probability of a stock reaching a certain price level or the probability of a particular economic indicator having a certain value.

The binary entropy function is often used in conjunction with other technical analysis tools, such as statistical analysis and machine learning algorithms, to make more informed trading decisions. It can help traders and investors identify patterns and trends in the market, and make more accurate predictions about the direction of prices.

Here is the Bernoulli Process code snippet translated from Trading pinescript indicator which explores the Bernoulli Function/Distribution), and combined with the Shannon Entropy measurement

In case you need a primer for Bernoulli Distribution. Start here

```
//////////////////////////////////////////////////////////
//Coded By Rajandran R - Founder - Marketcalls //
//Co-Creator - www.algomojo.com //
//Creation Date - 01st Sep 2020 //
//////////////////////////////////////////////////////////
_SECTION_BEGIN("Bernoulli Entropy function");
src = ParamField("Source");
len = Param("Length",22,1,100,1);
range = Param("Range",0.67,0.01,1,0.01);
average = Param("Average",88,1,100,1);
vPR = Param("Percent Rank Limit",5,1,10,1);
cr = src/sum(src,len); //source, typ close, percent of close, measured over summation period
vr = log(volume)/sum(log(volume),len) ; //volume data, percent of volume, measured of summation period
vr2 = min(max(percentrank(vr,average)/100,0.001),0.999) ; //cutting out 100% and 0% readings, changing to +/-3sigma
cr2 = min(max(percentrank(cr,average)/100,0.001),0.999) ;
infoc = sum((cr2*log10(cr2)/log10(2)) - (1-cr2)*log10(1-cr2)/log10(2),len); //p(close)*log2(p(close)) - (1-p(close))*log2(1-p(close))
infov = sum((vr2*log10(vr2)/log10(2)) - (1-vr2)*log10(1-vr2)/log10(2),len);
info2 = infoc - infov ;
color = IIf(info2>range, colorGreen, IIf(info2<-range,colorRed,colorGrey40));
Plot(info2,"Info",color,styleHistogram | styleThick);
Plot(infoc,"Price",colorBlue);
Plot(-infov,"Volume",colorOrange);
hvp = percentrank(info2,average);
PlotShapes(IIf(hvp<vPR, shapeUpArrow, shapeNone),colorlime, 0,info2, Offset=-25);
PlotShapes(IIf(hvp>(100-vPR), shapeDownArrow, shapeNone),colorred, 0,info2, Offset=-25);
SetChartOptions(0,chartShowArrows|chartShowDates);
_SECTION_END();
```

**Simple Trading System Based on Bernoulli Entropy function**

```
//////////////////////////////////////////////////////////
//Coded By Rajandran R - Founder - Marketcalls //
//Co-Creator - www.algomojo.com //
//Creation Date - 01st Sep 2020 //
//////////////////////////////////////////////////////////
_SECTION_BEGIN("Trading System Based on Bernoulli Entropy function");
src = ParamField("Source");
len = Param("Length",22,1,100,1);
range = Param("Range",0.67,0.01,1,0.01);
average = Param("Average",88,1,100,1);
vPR = Param("Percent Rank Limit",5,1,10,1);
cr = src/sum(src,len); //source, typ close, percent of close, measured over summation period
vr = log(volume)/sum(log(volume),len) ; //volume data, percent of volume, measured of summation period
vr2 = min(max(percentrank(vr,average)/100,0.001),0.999) ; //cutting out 100% and 0% readings, changing to +/-3sigma
cr2 = min(max(percentrank(cr,average)/100,0.001),0.999) ;
infoc = sum((cr2*log10(cr2)/log10(2)) - (1-cr2)*log10(1-cr2)/log10(2),len); //p(close)*log2(p(close)) - (1-p(close))*log2(1-p(close))
infov = sum((vr2*log10(vr2)/log10(2)) - (1-vr2)*log10(1-vr2)/log10(2),len);
info2 = infoc - infov ;
color = IIf(info2>range, colorGreen, IIf(info2<-range,colorRed,colorGrey40));
//Plot(info2,"Info",color,styleHistogram | styleThick);
//Plot(infoc,"Price",colorBlue);
//Plot(-infov,"Volume",colorOrange);
hvp = percentrank(info2,average);
Buy = info2>range;
sell = info2<-range;
Buy = ExRem(Buy,Sell);
Sell = ExRem(Sell,Buy);
/* Plot Buy and Sell Signal Arrows */
PlotShapes(IIf(Buy, shapeSquare, shapeNone),colorGreen, 0, L, Offset=-40);
PlotShapes(IIf(Buy, shapeSquare, shapeNone),colorLime, 0,L, Offset=-50);
PlotShapes(IIf(Buy, shapeUpArrow, shapeNone),colorWhite, 0,L, Offset=-45);
PlotShapes(IIf(Sell, shapeSquare, shapeNone),colorRed, 0, H, Offset=40);
PlotShapes(IIf(Sell, shapeSquare, shapeNone),colorOrange, 0,H, Offset=50);
PlotShapes(IIf(Sell, shapeDownArrow, shapeNone),colorWhite, 0,H, Offset=-45);
SetChartOptions(0,chartShowArrows|chartShowDates);
_N(Title = StrFormat("{{NAME}} - {{INTERVAL}} {{DATE}} Open %g, Hi %g, Lo %g, Close %g (%.1f%%) {{VALUES}}", O, H, L, C, SelectedValue( ROC( C, 1 ) ) ));
Plot( C, "Close", color, styleNoTitle | ParamStyle("Style") | GetPriceStyle() );
_SECTION_END();
```