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Kurtosis Indicator

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.
Pine Script™ library
by 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.
Pine Script™ library
by 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.
Pine Script™ library
by 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.
Pine Script™ strategy
by 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.
Pine Script™ indicator
by HPotter
1