The inverse or hyperbolic tangent function is a type os sigmoid function (sometime called squashing function), those types of functions can rescale a result in a certain range and are widely used in artificial intelligence. More in depth the can make the of a time series normally distributed, in practice if you apply the to the between a time series and a linear function you will end up with an estimate of the z-score of the time series. The inverse transform however can do the contrary, it can take the z-score and transform it into a rough estimate of the , if your z-score is not smooth then you will have a non-smooth estimate of the , that's quite nice no ?
The inverse of the z-score will produce results in a range of 1/-1, here however i will rescale in a range of 100/0 because its a standard range for oscillators in . Values over 80 indicate an overbought market, under 20 an oversold market. The smooth option in the indicator settings will make the indicator use a linearly as input thus resulting in a smoother result.
The indicator with smooth option.
I presented a new oscillator indicator who use the inverse of a z-score. Using the and its inverse can give a new shape to your indicator, make sure to control the scale of your indicator before applying the , the inverse transform should be applied to values in range of 1/-1 but you can use higher limits (2/-2,3/-3...), however remember that higher limits will approximate an heavy side step function (square shape). I hope you will find an use to this indicator.
Thanks for reading !
In true TradingView spirit, the author of this script has published it open-source, so traders can understand and verify it. Cheers to the author! You may use it for free, but reuse of this code in a publication is governed by House Rules. You can favorite it to use it on a chart.
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You can also check out some of the indicators I made for luxalgo : https://www.tradingview.com/u/LuxAlgo/#published-scripts