Normal Distribution Curve

This Normal Distribution Curve is designed to overlay a simple normal distribution curve on top of any TradingView indicator. This curve represents a probability distribution for a given dataset and can be used to gain insights into the likelihood of various data levels occurring within a specified range, providing traders and investors with a clear visualization of the distribution of values within a specific dataset. With the only inputs being the variable source and plot colour, I think this is by far the simplest and most intuitive iteration of any statistical analysis based indicator I've seen here!

Traders can quickly assess how data clusters around the mean in a bell curve and easily see the percentile frequency of the data; or perhaps with both and upper and lower peaks identify likely periods of upcoming volatility or mean reversion. Facilitating the identification of outliers was my main purpose when creating this tool, I believed fixed values for upper/lower bounds within most indicators are too static and do not dynamically fit the vastly different movements of all assets and timeframes - and being able to easily understand the spread of information simplifies the process of identifying key regions to take action.

The curve's tails, representing the extreme percentiles, can help identify outliers and potential areas of price reversal or trend acceleration. For example using the RSI which typically has static levels of 70 and 30, which will be breached considerably more on a less liquid or more volatile asset and therefore reduce the actionable effectiveness of the indicator, likewise for an asset with little to no directional volatility failing to ever reach this overbought/oversold areas. It makes considerably more sense to look for the top/bottom 5% or 10% levels of outlying data which are automatically calculated with this indicator, and may be a noticeable distance from the 70 and 30 values, as regions to be observing for your investing.

This normal distribution curve employs percentile linear interpolation to calculate the distribution. This interpolation technique considers the nearest data points and calculates the price values between them. This process ensures a smooth curve that accurately represents the probability distribution, even for percentiles not directly present in the original dataset; and applicable to any asset regardless of timeframe. The lookback period is set to a value of 5000 which should ensure ample data is taken into calculation and consideration without surpassing any TradingView constraints and limitations, for datasets smaller than this the indicator will adjust the length to just include all data. The labels providing the percentile and average levels can also be removed in the style tab if preferred.

Additionally, as an unplanned benefit is its applicability to the underlying price data as well as any derived indicators. Turning it into something comparable to a volume profile indicator but based on the time an assets price was within a specific range as opposed to the volume. This can therefore be used as a tool for identifying potential support and resistance zones, as well as areas that mark market inefficiencies as price rapidly accelerated through. This may then give a cleaner outlook as it eliminates the potential drawbacks of volume based profiles that maybe don't collate all exchange data or are misrepresented due to large unforeseen increases/decreases underlying capital inflows/outflows.

Thanks to @ALifeToMake, @Bjorgum, vgladkov on stackoverflow (and possibly some chatGPT!) for all the assistance in bringing this indicator to life. I really hope every user can find some use from this and help bring a unique and data driven perspective to their decision making. And make sure to please share any original implementaions of this tool too! If you've managed to apply this to the average price change once you've entered your position to better manage your trade management, or maybe overlaying on an implied volatility indicator to identify potential options arbitrage opportunities; let me know! And of course if anyone has any issues, questions, queries or requests please feel free to reach out! Thanks and enjoy.

Nota Keluaran:

The best way to use this tool is to add it to your chart, move it to an existing price or indicator, right click on the indicator to merge all scales on the right, and then alter the indicator source to whatever you're trying to calculate over. This way you can see directly the correlation!

New update removes old labels to prevent overlapping.

Nota Keluaran:

Altered the lookback length calculation to prevent errors on charts with limited data history.
Added a filter to prevent pushing na(src) values to plot array and misaligning the line lengths.
Simplified and corrected line.set() plotting method to work on charts with limited data history.