Empiece

Skewness

GaussianDistributionLibrary "GaussianDistribution" This library defines a custom type `distr` representing a Gaussian (or other statistical) distribution. It provides methods to calculate key statistical moments and scores, including mean, median, mode, standard deviation, variance, skewness, kurtosis, and Z-scores. This library is useful for analyzing probability distributions in financial data. Disclaimer: I am not a mathematician, but I have implemented this library to the best of my understanding and capacity. Please be indulgent as I tried to translate statistical concepts into code as accurately as possible. Feedback, suggestions, and corrections are welcome to improve the reliability and robustness of this library. mean(source, length)   Calculate the mean (average) of the distribution   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics)   Returns: Mean (μ) stdev(source, length)   Calculate the standard deviation (σ) of the distribution   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics)   Returns: Standard deviation (σ) skewness(source, length, mean, stdev)   Calculate the skewness (γ₁) of the distribution   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics)      mean (float) : the mean (average) of the distribution      stdev (float) : the standard deviation (σ) of the distribution @return Skewness (γ₁) skewness(source, length)   Overloaded skewness to calculate from source and length   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics) @return Skewness (γ₁) mode(mean, stdev, skewness)   Estimate mode - Most frequent value in the distribution (approximation based on skewness)   Parameters:      mean (float) : the mean (average) of the distribution      stdev (float) : the standard deviation (σ) of the distribution      skewness (float) : the skewness (γ₁) of the distribution @return Mode mode(source, length)   Overloaded mode to calculate from source and length   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics) @return Mode median(mean, stdev, skewness)   Estimate median - Middle value of the distribution (approximation)   Parameters:      mean (float) : the mean (average) of the distribution      stdev (float) : the standard deviation (σ) of the distribution      skewness (float) : the skewness (γ₁) of the distribution @return Median median(source, length)   Overloaded median to calculate from source and length   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics) @return Median variance(stdev)   Calculate variance (σ²) - Square of the standard deviation   Parameters:      stdev (float) : the standard deviation (σ) of the distribution @return Variance (σ²) variance(source, length)   Overloaded variance to calculate from source and length   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics) @return Variance (σ²) kurtosis(source, length, mean, stdev)   Calculate kurtosis (γ₂) - Degree of "tailedness" in the distribution   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics)      mean (float) : the mean (average) of the distribution      stdev (float) : the standard deviation (σ) of the distribution @return Kurtosis (γ₂) kurtosis(source, length)   Overloaded kurtosis to calculate from source and length   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics) @return Kurtosis (γ₂) normal_score(source, mean, stdev)   Calculate Z-score (standard score) assuming a normal distribution   Parameters:      source (float) : Distribution source (typically a price or indicator series)      mean (float) : the mean (average) of the distribution      stdev (float) : the standard deviation (σ) of the distribution @return Z-Score normal_score(source, length)   Overloaded normal_score to calculate from source and length   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics) @return Z-Score non_normal_score(source, mean, stdev, skewness, kurtosis)   Calculate adjusted Z-score considering skewness and kurtosis   Parameters:      source (float) : Distribution source (typically a price or indicator series)      mean (float) : the mean (average) of the distribution      stdev (float) : the standard deviation (σ) of the distribution      skewness (float) : the skewness (γ₁) of the distribution      kurtosis (float) : the "tailedness" in the distribution @return Z-Score non_normal_score(source, length)   Overloaded non_normal_score to calculate from source and length   Parameters:      source (float) : Distribution source (typically a price or indicator series)      length (int) : Window length for the distribution (must be >= 30 for meaningful statistics) @return Z-Score method init(this)   Initialize all statistical fields of the `distr` type   Namespace types: distr   Parameters:      this (distr) method init(this, source, length)   Overloaded initializer to set source and length   Namespace types: distr   Parameters:      this (distr)      source (float)      length (int) distr   Custom type to represent a Gaussian distribution   Fields:      source (series float) : Distribution source (typically a price or indicator series)      length (series int) : Window length for the distribution (must be >= 30 for meaningful statistics)      mode (series float) : Most frequent value in the distribution      median (series float) : Middle value separating the greater and lesser halves of the distribution      mean (series float) : μ (1st central moment) - Average of the distribution      stdev (series float) : σ or standard deviation (square root of the variance) - Measure of dispersion      variance (series float) : σ² (2nd central moment) - Squared standard deviation      skewness (series float) : γ₁ (3rd central moment) - Asymmetry of the distribution      kurtosis (series float) : γ₂ (4th central moment) - Degree of "tailedness" relative to a normal distribution      normal_score (series float) : Z-score assuming normal distribution      non_normal_score (series float) : Adjusted Z-score considering skewness and kurtosis
Biblioteca de Pine Script™
por Horrorin
NormalDistributionFunctionsLibrary "NormalDistributionFunctions" The NormalDistributionFunctions library encompasses a comprehensive suite of statistical tools for financial market analysis. It provides functions to calculate essential statistical measures such as mean, standard deviation, skewness, and kurtosis, alongside advanced functionalities for computing the probability density function (PDF), cumulative distribution function (CDF), Z-score, and confidence intervals. This library is designed to assist in the assessment of market volatility, distribution characteristics of asset returns, and risk management calculations, making it an invaluable resource for traders and financial analysts. meanAndStdDev(source, length)   Calculates and returns the mean and standard deviation for a given data series over a specified period.   Parameters:      source (float) : float: The data series to analyze.      length (int) : int: The lookback period for the calculation.   Returns: Returns an array where the first element is the mean and the second element is the standard deviation of the data series for the given period. skewness(source, mean, stdDev, length)   Calculates and returns skewness for a given data series over a specified period.   Parameters:      source (float) : float: The data series to analyze.      mean (float) : float: The mean of the distribution.      stdDev (float) : float: The standard deviation of the distribution.      length (int) : int: The lookback period for the calculation.   Returns: Returns skewness value kurtosis(source, mean, stdDev, length)   Calculates and returns kurtosis for a given data series over a specified period.   Parameters:      source (float) : float: The data series to analyze.      mean (float) : float: The mean of the distribution.      stdDev (float) : float: The standard deviation of the distribution.      length (int) : int: The lookback period for the calculation.   Returns: Returns kurtosis value pdf(x, mean, stdDev)   pdf: Calculates the probability density function for a given value within a normal distribution.   Parameters:      x (float) : float: The value to evaluate the PDF at.      mean (float) : float: The mean of the distribution.      stdDev (float) : float: The standard deviation of the distribution.   Returns: Returns the probability density function value for x. cdf(x, mean, stdDev)   cdf: Calculates the cumulative distribution function for a given value within a normal distribution.   Parameters:      x (float) : float: The value to evaluate the CDF at.      mean (float) : float: The mean of the distribution.      stdDev (float) : float: The standard deviation of the distribution.   Returns: Returns the cumulative distribution function value for x. confidenceInterval(mean, stdDev, size, confidenceLevel)   Calculates the confidence interval for a data series mean.   Parameters:      mean (float) : float: The mean of the data series.      stdDev (float) : float: The standard deviation of the data series.      size (int) : int: The sample size.      confidenceLevel (float) : float: The confidence level (e.g., 0.95 for 95% confidence).   Returns: Returns the lower and upper bounds of the confidence interval.
Biblioteca de Pine Script™
por tkarolak
4
Normal Distribution Asymmetry & Volatility ZonesNormal Distribution Asymmetry & Volatility Zones Indicator provides insights into the skewness of a price distribution and identifies potential volatility zones in the market. The indicator calculates the skewness coefficient, indicating the asymmetry of the price distribution, and combines it with a measure of volatility to define buy and sell zones. The key features of this indicator include : Skewness Calculation : It calculates the skewness coefficient, a statistical measure that reveals whether the price distribution is skewed to the left (negative skewness) or right (positive skewness). Volatility Zones : Based on the skewness and a user-defined volatility threshold, the indicator identifies buy and sell zones where potential price movements may occur. Buy zones are marked when skewness is negative and prices are below a volatility threshold. Sell zones are marked when skewness is positive and prices are above the threshold. Signal Source Selection : Traders can select the source of price data for analysis, allowing flexibility in their trading strategy. Customizable Parameters : Users can adjust the length of the distribution, the volatility threshold, and other parameters to tailor the indicator to their specific trading preferences and market conditions. Visual Signals : Buy and sell zones are visually displayed on the chart, making it easy to identify potential trade opportunities. Background Color : The indicator changes the background color of the chart to highlight significant zones, providing a clear visual cue for traders. By combining skewness analysis and volatility thresholds, this indicator offers traders a unique perspective on potential market movements, helping them make informed trading decisions. Please note that trading involves risks, and this indicator should be used in conjunction with other analysis and risk management techniques.
Indicador de Pine Script™
por tkarolak
3
Rolling QuartilesThis script will continuously draw a boxplot to represent quartiles associated with data points in the current rolling window. Description : A quartile is a statistical term that refers to the division of a dataset based on percentiles. Q1 : Quartile 1 - 25th percentile Q2 : Quartile 2 - 50th percentile, as known as the median Q3 : Quartile 3 - 75th percentile Other points to note: Q0: the minimum Q4: the maximum Other properties : - Q1 to Q3: a range is known as the interquartile range ( IQR ). It describes where 50% of data approximately lie. - Line segments connecting IQR to min and max (Q0→Q1, and Q3→Q4) are known as whiskers . Data lying outside the whiskers are considered as outliers. However, such extreme values will not be found in a rolling window because whenever new datapoints are introduced to the dataset, the oldest values will get dropped out, leaving Q0 and Q4 to always point to the observable min and max values. Applications : This script has a feature that allows moving percentiles (moving values of Q1, Q2, and Q3) to be shown. This can be applied for trading in ways such as: - Q2: as alternative to a SMA that uses the same lookback period. We know that the Mean (SMA) is highly sensitive to extreme values. On the other hand, Median (Q2) is less affected by skewness. Putting it together, if the SMA is significantly lower than Q2, then price is regarded as negatively skewed; prices of a few candles are likely exceptionally lower. Vice versa when price is positively skewed. - Q1 and Q3: as lower and upper bands. As mentioned above, the IQR covers approximately 50% of data within the rolling window. If price is normally distributed, then Q1 and Q3 bands will overlap a bollinger band configured with +/- 0.67x standard deviations (modifying default: 2) above and below the mean. - The boxplot, combined with TradingView's builtin bar replay feature, makes a great tool for studies purposes. This helps visualization of price at a chosen instance of time. Speaking of which, it can also be used in conjunction with a fixed volume profile to compare and contrast the effects (in terms of price range) with and without consideration of weights by volume. Parameters : - Lookback: The size of the rolling window. - Offset: Location of boxplot, right hand side relative to recent bar. - Source data: Data points for observation, default is closing price - Other options such as color, and whether to show/hide various lines.
Indicador de Pine Script™
por DojiEmoji
2
MomentsLibrary "Moments" Based on Moments (Mean,Variance,Skewness,Kurtosis) . Rewritten for Pinescript v5. logReturns(src) Calculates log returns of a series (e.g log percentage change)   Parameters:      src : Source to use for the returns calculation (e.g. close).   Returns: Log percentage returns of a series mean(src, length) Calculates the mean of a series using ta.sma   Parameters:      src : Source to use for the mean calculation (e.g. close).      length : Length to use mean calculation (e.g. 14).   Returns: The sma of the source over the length provided. variance(src, length) Calculates the variance of a series   Parameters:      src : Source to use for the variance calculation (e.g. close).      length : Length to use for the variance calculation (e.g. 14).   Returns: The variance of the source over the length provided. standardDeviation(src, length) Calculates the standard deviation of a series   Parameters:      src : Source to use for the standard deviation calculation (e.g. close).      length : Length to use for the standard deviation calculation (e.g. 14).   Returns: The standard deviation of the source over the length provided. skewness(src, length) Calculates the skewness of a series   Parameters:      src : Source to use for the skewness calculation (e.g. close).      length : Length to use for the skewness calculation (e.g. 14).   Returns: The skewness of the source over the length provided. kurtosis(src, length) Calculates the kurtosis of a series   Parameters:      src : Source to use for the kurtosis calculation (e.g. close).      length : Length to use for the kurtosis calculation (e.g. 14).   Returns: The kurtosis of the source over the length provided. skewnessStandardError(sampleSize) Estimates the standard error of skewness based on sample size   Parameters:      sampleSize : The number of samples used for calculating standard error.   Returns: The standard error estimate for skewness based on the sample size provided. kurtosisStandardError(sampleSize) Estimates the standard error of kurtosis based on sample size   Parameters:      sampleSize : The number of samples used for calculating standard error.   Returns: The standard error estimate for kurtosis based on the sample size provided. skewnessCriticalValue(sampleSize) Estimates the critical value of skewness based on sample size   Parameters:      sampleSize : The number of samples used for calculating critical value.   Returns: The critical value estimate for skewness based on the sample size provided. kurtosisCriticalValue(sampleSize) Estimates the critical value of kurtosis based on sample size   Parameters:      sampleSize : The number of samples used for calculating critical value.   Returns: The critical value estimate for kurtosis based on the sample size provided.
Biblioteca de Pine Script™
por nolantait
ArrayStatisticsLibrary "ArrayStatistics" Statistic Functions using arrays. rms(sample) Root Mean Squared Parameters: sample : float array, data sample points. Returns: float skewness_pearson1(sample) Pearson's 1st Coefficient of Skewness. Parameters: sample : float array, data sample. Returns: float skewness_pearson2(sample) Pearson's 2nd Coefficient of Skewness. Parameters: sample : float array, data sample. Returns: float pearsonr(sample_a, sample_b) Pearson correlation coefficient measures the linear relationship between two datasets. Parameters: sample_a : float array, sample with data. sample_b : float array, sample with data. Returns: float p kurtosis(sample) Kurtosis of distribution. Parameters: sample : float array, data sample. Returns: float range_int(sample, percent) Get range around median containing specified percentage of values. Parameters: sample : int array, Histogram array. percent : float, Values percentage around median. Returns: tuple with , Returns the range which containes specifies percentage of values.
Biblioteca de Pine Script™
por RicardoSantos
1
Expected Range and SkewThis is an open source and updated version of my previous "Confidence Interval" script. This script provides you with the expected range over a given time period in the future and the skew of that range. For example, if you wanted to know the expected 1 standard deviation range of MSFT over the next 20 days, this will tell you that. Additionally, this script will also tell you the skew of the expected range. How to use this script: 1) Enter the length, this will determine the number of data points used in the calculation of the expected range. 2) Enter the amount of time you want projected forward in minutes, hours, and days. 3) Input standard deviation of the expected range. 4) Pick the type of data you want shown from the dropdown menu. Your choices are either the expected range or the skew of the expected range. 5) Enter the x and y coordinates of the label (optional). This is useful so it doesn't impede your view of the plot. Here are a few notes about this script: First, the expected range line gives you the width of said range (upper bound - lower bound), and the label will tell you specifically what the upper and lower bounds of the expected range are. Second, this script will work on any of the default timeframes, but you need to be careful with how far out you try to project the expected range depending on the timeframe you're using. For example, if you're using the 1min timeframe, it probably won't do you any good trying to project the expected range over the next 20 days; or if you're using the daily timeframe it doesn't make sense to try to project the expected range for the next 5 hours. You can tell if the time horizon you're trying to project doesn't work well with the chart timeframe you're using if the current price is outside of either the upper or lower bounds provided in the label. If the current price is within the upper and lower bounds provided in the label, then the time horizon that you're projecting over is reasonable for the chart timeframe you're using. Third, this script does not countdown automatically, so the time provided in the label will stay the same. For example, in the picture above, the expected range of Dow Futures over the next 23 days from January 12th, 2021 is calculated. But when tomorrow comes it won't count down to 22 days, instead it will show the range over the next 23 days from January 13th, 2021. So if you want the time horizon to change as time goes on you will have to update this yourself manually. Lastly, if you try to set an alert on this script, you will get a warning about it possibly repainting. This is because of the label, not the plot itself. The label constantly updates itself, which triggers the warning. I tested setting alerts on this script both with and without the inclusion of the label, and without the label the repainting warning did not occur. So remember, if you set an alert on this script you will get a warning about it possibly repainting, but this is because of the label constantly updating, not the plot itself.
Indicador de Pine Script™
por SegaRKO
6