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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
ספריית Pine Script™
מאת ‎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.
ספריית Pine Script™
מאת ‎tkarolak‎
4
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.
ספריית Pine Script™
מאת ‎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.
ספריית Pine Script™
מאת ‎RicardoSantos‎
1
Combo Backtest 123 Reversal & FSK (Fast and Slow Kurtosis) This is combo strategies for get a cumulative signal. First strategy This System was created from the Book "How I Tripled My Money In The Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies. The strategy buys at market, if close price is higher than the previous close during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50. The strategy sells at market, if close price is lower than the previous close price during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50. Second strategy This indicator plots the Fast & Slow Kurtosis. The Kurtosis is a market sentiment indicator. The Kurtosis is constructed from three different parts. The Kurtosis, the Fast Kurtosis(FK), and the Fast/Slow Kurtosis(FSK). WARNING: - For purpose educate only - This script to change bars colors.
אסטרטגיית Pine Script™
מאת ‎HPotter‎
1
Combo Strategy 123 Reversal & FSK (Fast and Slow Kurtosis) This is combo strategies for get a cumulative signal. First strategy This System was created from the Book "How I Tripled My Money In The Futures Market" by Ulf Jensen, Page 183. This is reverse type of strategies. The strategy buys at market, if close price is higher than the previous close during 2 days and the meaning of 9-days Stochastic Slow Oscillator is lower than 50. The strategy sells at market, if close price is lower than the previous close price during 2 days and the meaning of 9-days Stochastic Fast Oscillator is higher than 50. Second strategy This indicator plots the Fast & Slow Kurtosis. The Kurtosis is a market sentiment indicator. The Kurtosis is constructed from three different parts. The Kurtosis, the Fast Kurtosis(FK), and the Fast/Slow Kurtosis(FSK). WARNING: - For purpose educate only - This script to change bars colors.
אינדיקטור Pine Script™
מאת ‎HPotter‎
1