"In a standard normal distribution, the range covered by three standard deviations (3σ, where σ r .."

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1.3 Normal statistical method

compilation of industrial mathematics algorithms(4)

In a standard normal distribution, the range covered by three standard deviations (3σ, where σ represents one standard deviation) can encompass 99.7% of the data. Therefore, data points outside 3σ can be considered outliers.

One standard deviation encompasses 68% of the data.

Two standard deviations encompass 95% of the data.

Three standard deviations encompass 99.7% of the data.

The characteristics of a normal distribution determine that the data points outside a range of n standard deviations are uncommon and can be considered anomalies.

Select a threshold-mode anomaly function:

TA[tu,td](x)=max(x-tu, td-x,0)/(tu-td)

The method to calculate tu and td using X[-k]_i is as follows:

a=avg(X[-k]_i)
σ=std(X[-k]_i)
tu=a+n*σ
td=a-n*σ

Where, a is the average of X[-k]_i, σ is the standard deviation of X[-k]_i, and n is a multiple of the standard deviation. Modifying n can adjust the size of tu and td.

The anomaly score od is calculated as follows:

od=max(x_i-tu, td-x_i,0)/(tu-td)

SPL routine:

	A	B
1	=data=file(“1Ddata.csv”).import@tci().to(100)
2	=n=3	/Multiple of standard deviation
3	=ldata=data.m(:100)	/Learning data X[-k]_i (interval of 100)
4	=xi=data(101)	/x_i
5	=a=A3.avg()	/Average a
6	=sigma=sqrt(var@s(A3))	/Standard deviation σ
7	=td=a-n*sigma	/Lower limit td
8	=tu=a+n*sigma	/Upper limit tu
9	=od=max(xi-tu,td-xi,0)/(tu-td)	/Anomaly score od