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Price Legs: Average Heights; 'Smart ATR'Price Legs: Average Heights; 'Smart ATR'. Consol Range Gauge ~~ Indicator to show small and large price legs (based on short and long input pivot lengths), and calculating the average heights of these price legs; counting legs from user-input start time ~~ //Premise: Wanted to use this as something like a 'Smart ATR': where the average/typical range of a distinct & dynamic price leg could be calculated based on a user-input time interval (as opposed to standard ATR, which is simply the average range over a consistent repeating period, with no regard to market structure). My instinct is that this would be most useful for consolidated periods & range trading: giving the trader an idea of what the typical size of a price leg might be in the current market state (hence in the title, Consol Range gauge) //Features & User inputs: -Start time: confirm input when loading indicator by clicking on the chart. Then drag the vertical line to change start time easily. -Large Legs (toggle on/off) and user-input pivot lookback/lookforward length (larger => larger legs) -Small Legs (toggle on/off) and user-input pivot lookback/lookforward length (smaller => smaller legs) -Display Stats table: toggle on/off: simple view- shows the averages of large (up & down), small (up & down), and combined (for each). -Extended stats table: toggle on/off option to show the averages of the last 3 legs of each category (up/down/large/small/combined) -Toggle on/off Time & Price chart text labels of price legs (time in mins/hours/days; price in $ or pips; auto assigned based on asset) -Table position: user choice. //Notes & tips: -Using custom start time along with replay mode, you can select any arbitrary chunk of price for the purpose of backtesting. -Play around with the pivot lookback lengths to find price legs most suitable to the current market regime (consolidating/trending; high volatility/ low volatility) -Single bar price legs will never be counted: they must be at least 2 bars from H>>L or L>>H. //Credits: Thanks to @crypto_juju for the idea of applying statistics to this simple price leg indicator. Simple View: showing only the full averages (counting from Start time): View showing ONLY the large legs, with Time & Price labels toggled ON:

BenfordsLaw Library "BenfordsLaw" Methods to deal with Benford's law which states that a distribution of first and higher order digits of numerical strings has a characteristic pattern. "Benford's law is an observation about the leading digits of the numbers found in real-world data sets. Intuitively, one might expect that the leading digits of these numbers would be uniformly distributed so that each of the digits from 1 to 9 is equally likely to appear. In fact, it is often the case that 1 occurs more frequently than 2, 2 more frequently than 3, and so on. This observation is a simplified version of Benford's law. More precisely, the law gives a prediction of the frequency of leading digits using base-10 logarithms that predicts specific frequencies which decrease as the digits increase from 1 to 9." ~(2) --- reference: - 1: en.wikipedia.org - 2: brilliant.org - 4: github.com cumsum_difference(a, b) Calculate the cumulative sum difference of two arrays of same size. Parameters: a (float ) : `array` List of values. b (float ) : `array` List of values. Returns: List with CumSum Difference between arrays. fractional_int(number) Transform a floating number including its fractional part to integer form ex:. `1.2345 -> 12345`. Parameters: number (float) : `float` The number to transform. Returns: Transformed number. split_to_digits(number, reverse) Transforms a integer number into a list of its digits. Parameters: number (int) : `int` Number to transform. reverse (bool) : `bool` `default=true`, Reverse the order of the digits, if true, last will be first. Returns: Transformed number digits list. digit_in(number, digit) Digit at index. Parameters: number (int) : `int` Number to parse. digit (int) : `int` `default=0`, Index of digit. Returns: Digit found at the index. digits_from(data, dindex) Process a list of `int` values and get the list of digits. Parameters: data (int ) : `array` List of numbers. dindex (int) : `int` `default=0`, Index of digit. Returns: List of digits at the index. digit_counters(digits) Score digits. Parameters: digits (int ) : `array` List of digits. Returns: List of counters per digit (1-9). digit_distribution(counters) Calculates the frequency distribution based on counters provided. Parameters: counters (int ) : `array` List of counters, must have size(9). Returns: Distribution of the frequency of the digits. digit_p(digit) Expected probability for digit according to Benford. Parameters: digit (int) : `int` Digit number reference in range `1 -> 9`. Returns: Probability of digit according to Benford's law. benfords_distribution() Calculated Expected distribution per digit according to Benford's Law. Returns: List with the expected distribution. benfords_distribution_aprox() Aproximate Expected distribution per digit according to Benford's Law. Returns: List with the expected distribution. test_benfords(digits, calculate_benfords) Tests Benford's Law on provided list of digits. Parameters: digits (int ) : `array` List of digits. calculate_benfords (bool) Returns: Tuple with: - Counters: Score of each digit. - Sample distribution: Frequency for each digit. - Expected distribution: Expected frequency according to Benford's. - Cumulative Sum of difference: to_table(digits, _text_color, _border_color, _frame_color) Parameters: digits (int ) _text_color (color) _border_color (color) _frame_color (color)

Profitable Supertrend v0.1 - Alpha This a script to try detect the best combination of supertrend parameters in a space of time. Sadly the script is slow. Evaluate all possibilities params is hard for a pinescript and my knowledge too. In some cases, when you want evaluate many time could be the script fails for timeout. Perhaps with time I could enhance. For this problem of speed the calculate of combinatios it's not complete: In factor use a increment of 0.2 in each param (0.1, 0.3, 0.5 ...) in period the increment for each value is 3. The range for factor it's from 3.0 to 12.0. The range of period it's from 10 to 43 My knowledge don't let me go more far. Perhaps with time I can enhance the script.

Reinforced RSI - The Quant Science This strategy was designed and written with the goal of showing and motivating the community how to integrate our 'Probabilities' module with their own script. We have recreated one of the simplest strategies used by many traders. The strategy only trades long and uses the overbought and oversold levels on the RSI indicator. We added stop losses and take profits to offer more dynamism to the strategy. Then the 'Probabilities' module was integrated to create a probabilistic reinforcement on each trade. Specifically, each trade is executed, only if the past probabilities of making a profitable trade is greater than or equal to 51%. This greatly increased the performance of the strategy by avoiding possible bad trades. The backtesting was calculated on the NASDAQ:TSLA , on 15 minutes timeframe. The strategy works on Tesla using the following parameters: 1. Lenght: 13 2. Oversold: 40 3. Overbought: 70 4. Lookback: 50 5. Take profit: 3% 6. Stop loss: 3% Time period: January 2021 to date. Our Probabilities Module, used in the strategy example:

Probabilities Module - The Quant Science This module can be integrate in your code strategy or indicator and will help you to calculate the percentage probability on specific event inside your strategy. The main goal is improve and simplify the workflow if you are trying to build a quantitative strategy or indicator based on statistics or reinforcement model. Logic The script made a simulation inside your code based on a single event. For single event mean a trading logic composed by three different objects: entry, take profit, stop loss. The script scrape in the past through a look back function and return the positive percentage probability about the positive event inside the data sample. In this way you are able to understand and calculate how many time (in percentage term) the conditions inside the single event are positive, helping to create your statistical edge. You can adjust the look back period in you user interface. How can set up the module for your use case At the top of the script you can find: 1. entry_condition : replace the default condition with your specific entry condition. 2. TPcondition_exit : replace the default condition with your specific take profit condition. 3. SLcondition_exit : replace the default condition with your specific stop loss condition.

Student's T-Distribution Bollinger Bands This study shows the prediction interval as Bollinger Bands using Student's T-distribution. This means that the bands will be wider when the data features higher variation, as well as when the sample size (in the form of length) is smaller. The bands will also be wider when the confidence level is lower. The opposite is also true. Assuming we set a confidence level of 0.99 and a source set to the close price, we could reasonably expect that 99% of the time the close price would fall between the upper and lower bounds. Because this is a general statistical method which requires a lot of math, the script has a tendency to be relatively slow, but should be eligible to be used in a wide variety of situations.

Saty ATR Levels This indicator uses the previous period close and +/- 1 ATR to display significant day, multiday, swing, and position trading levels including: - Trigger clouds for possibly going long/short @ 23.6 fib - Mid-range level at 61.8 fib - Full range level at +/- 1 ATR (from previous close) - Extension level at 161.8 fib Additionally, a convenient info table is provided that shows trend, range utilization, and numerical long/short values. This indicator is most beneficial when you combine it with price, volume, and trend analysis. For educational content please check out the indicator website at atrlevels.com. I am constantly improving this indicator, please use this one if you want to continue to get new features, bug fixes, and support.

Bar Statistics This script calculates and displays some bar statistics. For the bar length statistics, it takes every length of upper or lower movements and calculates their average (with SD), median, and max. That way, you can see whether there is a bias in the market or not. Eg.: If for 10 bars, the market moved 2 up, then 1 down, then 3 up, then 2 down, and 2 up, the average up bars length would be at 2.33, while the average for the down length would be at 1.5, showing that upper movements last longer than down movements. For the range statistics, it takes the true range of each bar and calculates where the close of the bar is in relation to the true low of it. So if the closing of the bar is at 10.0, the low is at 9.0, and the high is at 10.2, the candle closed in the upper third of the bar. This process is calculated for every bar and for both closing prices and open prices. It is very useful to locate biasses, and they can you a better view of the market, since for most of the time a bar will open on an extreme and close on another extreme. Eg.: Here on the DJI, we can see that for most of the time, a month opens at the lower third (near the low) and closes at the upper third (near the high). We can also see that it is very difficult for a month to open or close on the middle of the candle, showing how important the first and the last day are for determining the trend of the rest of the month.

Inferential Statistics And Quick Metrics For Strategy Analysis.Part of this script is used to calculate inferential statistics and metrics not available through the built in variables in the strategy tester. A label will be created on the last bar displaying important strategy results, so you can test and analyze strategies quicker. The built in strategy itself is just an example. You can copy and paste the metrics into any existing version 4 strategy and instantly use it** **Just be sure all the variable names are unique in your target script. I am looking for critique and would appreciate input on the statistical functions. I am aware that some of these functions are based on the assumption that the data is normally distributed. It's not meant to be perfect, but it is meant to be helpful. So if you think I can add or improve something to make it more helpful, let me know.