Estimation of the Nth percentile of a series
When working with built-in functions in TradingView we have to limit our length parameters to max 4999. In case we want to use a function on the whole available series (bar 0 all the way to the current bar), we can usually not do this without manually creating these calculations in our code. For things like mean or standard deviation, this is quite trivial, but for things like percentiles, this is usually very costly. In more complex scripts, this becomes impossible because of resource restrictions from the Pine Script execution servers.
One solution to this is to use an estimation algorithm to get close to the true percentile value. Therefore, I have ported this implementation of the P-Square algorithm to Pine Script. P-Square is a fast algorithm that does a good job at estimating percentiles in data streams. Here's the algorithms original paper.
The chart
On the chart we see:
Note: We can see that the returns are not normally distributed as we can see that one standard deviation is higher than the 84.1th percentile. One standard deviation should equal the 84.1th percentile if the data is normally distributed.
When working with built-in functions in TradingView we have to limit our length parameters to max 4999. In case we want to use a function on the whole available series (bar 0 all the way to the current bar), we can usually not do this without manually creating these calculations in our code. For things like mean or standard deviation, this is quite trivial, but for things like percentiles, this is usually very costly. In more complex scripts, this becomes impossible because of resource restrictions from the Pine Script execution servers.
One solution to this is to use an estimation algorithm to get close to the true percentile value. Therefore, I have ported this implementation of the P-Square algorithm to Pine Script. P-Square is a fast algorithm that does a good job at estimating percentiles in data streams. Here's the algorithms original paper.
The chart
On the chart we see:
- The returns of the series (blue scatter plot)
- The mean of the returns of the series (orange line)
- The standard deviation of the returns of the series (yellow line)
- The actual 84.1th percentile of the returns (white line)
- The estimatedl 84.1th percentile of the returns using the P-Square algorithm (green line)
Note: We can see that the returns are not normally distributed as we can see that one standard deviation is higher than the 84.1th percentile. One standard deviation should equal the 84.1th percentile if the data is normally distributed.
開源腳本
本著TradingView的真正精神,此腳本的創建者將其開源,以便交易者可以查看和驗證其功能。向作者致敬!雖然您可以免費使用它,但請記住,重新發佈程式碼必須遵守我們的網站規則。
免責聲明
這些資訊和出版物並不意味著也不構成TradingView提供或認可的金融、投資、交易或其他類型的意見或建議。請在使用條款閱讀更多資訊。
開源腳本
本著TradingView的真正精神,此腳本的創建者將其開源,以便交易者可以查看和驗證其功能。向作者致敬!雖然您可以免費使用它,但請記住,重新發佈程式碼必須遵守我們的網站規則。
免責聲明
這些資訊和出版物並不意味著也不構成TradingView提供或認可的金融、投資、交易或其他類型的意見或建議。請在使用條款閱讀更多資訊。