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Statistics

DailyDeviationLibrary "DailyDeviation" Helps in determining the relative deviation from the open of the day compared to the high or low values. hlcDeltaArrays(daysPrior, maxDeviation, spec, res) Retuns a set of arrays representing the daily deviation of price for a given number of days.   Parameters:      daysPrior : Number of days back to get the close from.      maxDeviation : Maximum deviation before a value is considered an outlier. A value of 0 will not filter results.      spec : session.regular (default), session.extended or other time spec.      res : The resolution (default = '1440').   Returns: Where OH = Open vs High, OL = Open vs Low, and OC = Open vs Close fromOpen(daysPrior, maxDeviation, comparison, spec, res) Retuns a value representing the deviation from the open (to the high or low) of the current day given number of days to measure from.   Parameters:      daysPrior : Number of days back to get the close from.      maxDeviation : Maximum deviation before a value is considered an outlier. A value of 0 will not filter results.      comparison : The value use in comparison to the current open for the day.      spec : session.regular (default), session.extended or other time spec.      res : The resolution (default = '1440').
Pine Script™ library
by Electrified
VolatilityLibrary "Volatility" Functions for determining if volatility (true range) is within or exceeds normal. The "True Range" (ta.tr) is used for measuring volatility. Values are normalized by the volume adjusted weighted moving average (VAWMA) to be more like percent moves than price. current(len) Returns the current price adjusted volatitlity ratio.   Parameters:      len : Number of bars to get a volume adjusted weighted average price. normal(len, maxDeviation, level, gapDays, spec, res) Returns the normal upper range of volatility. Compensates for overnight gaps within a regular session.   Parameters:      len : Number of bars to measure volatility.      maxDeviation : The limit of volatility before considered an outlier.      level : The amount of standard deviation after cleaning outliers to be considered within normal.      gapDays : The number of days in the past to measure overnight gap volaility.      spec : session.regular (default), session.extended or other time spec.      res : The resolution (default = '1440'). isNormal(len, maxDeviation, level, gapDays, spec, res) Returns true if the volatility (true range) is within normal levels. Compensates for overnight gaps within a regular session.   Parameters:      len : Number of bars to measure volatility.      maxDeviation : The limit of volatility before considered an outlier.      level : The amount of standard deviation after cleaning outliers to be considered within normal.      gapDays : The number of days in the past to measure overnight gap volaility.      spec : session.regular (default), session.extended or other time spec.      res : The resolution (default = '1440'). severity(len, maxDeviation, level, gapDays, spec, res) Returns ratio of the current value to the normal value. Compensates for overnight gaps within a regular session.   Parameters:      len : Number of bars to measure volatility.      maxDeviation : The limit of volatility before considered an outlier.      level : The amount of standard deviation after cleaning outliers to be considered within normal.      gapDays : The number of days in the past to measure overnight gap volaility.      spec : session.regular (default), session.extended or other time spec.      res : The resolution (default = '1440').
Pine Script™ library
by Electrified
DataCleanerLibrary "DataCleaner" Functions for acquiring outlier levels and acquiring a cleaned version of a series. outlierLevel(src, len, level) Gets the (standard deviation) outlier level for a given series.   Parameters:      src : The series to average and add a multiple of the standard deviation to.      len : The The number of bars to measure.      level : The positive or negative multiple of the standard deviation to apply to the average. A positive number will be the upper boundary and a negative number will be the lower boundary.   Returns: The average of the series plus the multiple of the standard deviation. cleanUsing(src, result, len, maxDeviation) Returns an array representing the result series with (outliers provided by the source) removed.   Parameters:      src : The source series to read from.      result : The result series.      len : The maximum size of the resultant array.      maxDeviation : The positive or negative multiple of the standard deviation to apply to the average. A positive number will be the upper boundary and a negative number will be the lower boundary.   Returns: An array containing the cleaned series. clean(src, len, maxDeviation) Returns an array representing the source series with outliers removed.   Parameters:      src : The source series to read from.      len : The maximum size of the resultant array.      maxDeviation : The positive or negative multiple of the standard deviation to apply to the average. A positive number will be the upper boundary and a negative number will be the lower boundary.   Returns: An array containing the cleaned series. outlierLevelAdjusted(src, level, len, maxDeviation) Gets the (standard deviation) outlier level for a given series after a single pass of removing any outliers.   Parameters:      src : The series to average and add a multiple of the standard deviation to.      level : The positive or negative multiple of the standard deviation to apply to the average. A positive number will be the upper boundary and a negative number will be the lower boundary.      len : The The number of bars to measure.      maxDeviation : The optional standard deviation level to use when cleaning the series. The default is the value of the provided level.   Returns: The average of the series plus the multiple of the standard deviation.
Pine Script™ library
by Electrified
4
benchLibrary "bench" A simple banchmark library to analyse script performance and bottlenecks. Very useful if you are developing an overly complex application in Pine Script, or trying to optimise a library / function / algorithm... Supports artificial looping benchmarks (of fast functions) Supports integrated linear benchmarks (of expensive scripts) One important thing to note is that the Pine Script compiler will completely ignore any calculations that do not eventually produce chart output. Therefore, if you are performing an artificial benchmark you will need to use the bench.reference(value) function to ensure the calculations are executed. Please check the examples towards the bottom of the script. Quick Reference (Be warned this uses non-standard space characters to get the line indentation to work in the description!) ``` // Looping benchmark style benchmark = bench.new(samples = 500, loops = 5000) data = array.new_int() if bench.start(benchmark)   while bench.loop(benchmark)     array.unshift(data, timenow)   bench.mark(benchmark)   while bench.loop(benchmark)     array.unshift(data, timenow)   bench.mark(benchmark)   while bench.loop(benchmark)     array.unshift(data, timenow)   bench.stop(benchmark)   bench.reference(array.get(data, 0)) bench.report(benchmark, '1x array.unshift()') // Linear benchmark style benchmark = bench.new() data = array.new_int() bench.start(benchmark) for i = 0 to 1000   array.unshift(data, timenow) bench.mark(benchmark) for i = 0 to 1000   array.unshift(data, timenow) bench.stop(benchmark) bench.reference(array.get(data, 0)) bench.report(benchmark,'1000x array.unshift()') ``` Detailed Interface new(samples, loops) Initialises a new benchmark array   Parameters:      samples : int, the number of bars in which to collect samples      loops : int, the number of loops to execute within each sample   Returns: int , the benchmark array active(benchmark) Determing if the benchmarks state is active   Parameters:      benchmark : int , the benchmark array   Returns: bool, true only if the state is active start(benchmark) Start recording a benchmark from this point   Parameters:      benchmark : int , the benchmark array   Returns: bool, true only if the benchmark is unfinished loop(benchmark) Returns true until call count exceeds bench.new(loop) variable   Parameters:      benchmark : int , the benchmark array   Returns: bool, true while looping reference(number, string) Add a compiler reference to the chart so the calculations don't get optimised away   Parameters:      number : float, a numeric value to reference      string : string, a string value to reference mark(benchmark, number, string) Marks the end of one recorded interval and the start of the next   Parameters:      benchmark : int , the benchmark array      number : float, a numeric value to reference      string : string, a string value to reference stop(benchmark, number, string) Stop the benchmark, ending the final interval   Parameters:      benchmark : int , the benchmark array      number : float, a numeric value to reference      string : string, a string value to reference report(Prints, benchmark, title, text_size, position)   Parameters:      Prints : the benchmarks results to the screen      benchmark : int , the benchmark array      title : string, add a custom title to the report      text_size : string, the text size of the log console (global size vars)      position : string, the position of the log console (global position vars) unittest_bench(case) Cache module unit tests, for inclusion in parent script test suite. Usage: bench.unittest_bench(__ASSERTS)   Parameters:      case : string , the current test case and array of previous unit tests (__ASSERTS) unittest(verbose) Run the bench module unit tests as a stand alone. Usage: bench.unittest()   Parameters:      verbose : bool, optionally disable the full report to only display failures
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Pine Script™ library
by GeoffHammond
14
HurstExponentLibrary "HurstExponent" Library to calculate Hurst Exponent refactored from Hurst Exponent - Detrended Fluctuation Analysis demean(src) Calculates a series subtracted from the series mean.   Parameters:      src : The series used to calculate the difference from the mean (e.g. log returns).   Returns: The series subtracted from the series mean cumsum(src, length) Calculates a cumulated sum from the series.   Parameters:      src : The series used to calculate the cumulative sum (e.g. demeaned log returns).      length : The length used to calculate the cumulative sum (e.g. 100).   Returns: The cumulative sum of the series as an array aproximateLogScale(scale, length) Calculates an aproximated log scale. Used to save sample size   Parameters:      scale : The scale to aproximate.      length : The length used to aproximate the expected scale.   Returns: The aproximated log scale of the value rootMeanSum(cumulativeSum, barId, numberOfSegments) Calculates linear trend to determine error between linear trend and cumulative sum   Parameters:      cumulativeSum : The cumulative sum array to regress.      barId : The barId for the slice      numberOfSegments : The total number of segments used for the regression calculation   Returns: The error between linear trend and cumulative sum averageRootMeanSum(cumulativeSum, barId, length) Calculates the Root Mean Sum Measured for each block (e.g the aproximated log scale)   Parameters:      cumulativeSum : The cumulative sum array to regress and determine the average of.      barId : The barId for the slice      length : The length used for finding the average   Returns: The average root mean sum error of the cumulativeSum criticalValues(length) Calculates the critical values for a hurst exponent for a given length   Parameters:      length : The length used for finding the average   Returns: The critical value, upper critical value and lower critical value for a hurst exponent slope(cumulativeSum, length) Calculates the hurst exponent slope measured from root mean sum, scaled to log log plot using linear regression   Parameters:      cumulativeSum : The cumulative sum array to regress and determine the average of.      length : The length used for the hurst exponent sample size   Returns: The slope of the hurst exponent smooth(src, length) Smooths input using advanced linear regression   Parameters:      src : The series to smooth (e.g. hurst exponent slope)      length : The length used to smooth   Returns: The src smoothed according to the given length exponent(src, hurstLength) Wrapper function to calculate the hurst exponent slope   Parameters:      src : The series used for returns calculation (e.g. close)      hurstLength : The length used to calculate the hurst exponent (should be greater than 50)   Returns: The src smoothed according to the given length
Pine Script™ library
by nolantait
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
pNRTRLibrary "pNRTR" Provides functions for calculating Nick Rypock Trailing Reverse (NRTR) trend values with higher precision offsets for both low, and high points rather than the standard single offset. pnrtr(float low_offset = 0.2, float high_offset = 0.2, float value = close) low_offset Offset used for nrtr low_point calculations. Default is 0.2. high_offset Offset used for nrtr high_point calculations. Default is 0.2. value Variable used for nrtr point calculations. Default is close.
Pine Script™ library
by birdgineer
cacheLibrary "cache" A simple cache library to store key value pairs. Fed up of injecting and returning so many values all the time? Want to separate your code and keep it clean? Need to make an expensive calculation and use the results in numerous places? Want to throttle calculations or persist random values across bars or ticks? Then you've come to the right place. Or not! Up to you, I don't mind either way... ;) Check the helpers and unit tests in the script for further detail. Detailed Interface init(persistant) Initialises the syncronised cache key and value arrays   Parameters:      persistant : bool, toggles data persistance between bars and ticks   Returns: [string , float ], a tuple of both arrays set(keys, values, key, value) Sets a value into the cache   Parameters:      keys : string , the array of cache keys      values : float , the array of cache values      key : string, the cache key to create or update      value : float, the value to set has(keys, values, key) Checks if the cache has a key   Parameters:      keys : string , the array of cache keys      values : float , the array of cache values      key : string, the cache key to check   Returns: bool, true only if the key is found get(keys, values, key) Gets a keys value from the cache   Parameters:      keys : string , the array of cache keys      values : float , the array of cache values      key : string, the cache key to get   Returns: float, the stored value remove(keys, values, key) Removes a key and value from the cache   Parameters:      keys : string , the array of cache keys      values : float , the array of cache values      key : string, the cache key to remove count() Counts how many key value pairs in the cache   Returns: int, the total number of pairs loop(keys, values) Returns true for each value in the cache (use as the while loop expression)   Parameters:      keys : string , the array of cache keys      values : float , the array of cache values next(keys, values) Returns each key value pair on successive calls (use in the while loop)   Parameters:      keys : string , the array of cache keys      values : float , the array of cache values   Returns: , tuple of each key value pair clear(keys, values) Clears all key value pairs from the cache   Parameters:      keys : string , the array of cache keys      values : float , the array of cache values unittest_cache(case) Cache module unit tests, for inclusion in parent script test suite. Usage: log.unittest_cache(__ASSERTS)   Parameters:      case : string , the current test case and array of previous unit tests (__ASSERTS) unittest(verbose) Run the cache module unit tests as a stand alone. Usage: cache.unittest()   Parameters:      verbose : bool, optionally disable the full report to only display failures
Pine Script™ library
by GeoffHammond
3
FFTLibraryLibrary "FFTLibrary" contains a function for performing Fast Fourier Transform (FFT) along with a few helper functions. In general, FFT is defined for complex inputs and outputs. The real and imaginary parts of formally complex data are treated as separate arrays (denoted as x and y). For real-valued data, the array of imaginary parts should be filled with zeros. FFT function fft(x, y, dir) : Computes the one-dimensional discrete Fourier transform using an in-place complex-to-complex FFT algorithm . Note: The transform also produces a mirror copy of the frequency components, which correspond to the signal's negative frequencies.   Parameters:      x : float array, real part of the data, array size must be a power of 2      y : float array, imaginary part of the data, array size must be the same as x ; for real-valued input, y must be an array of zeros      dir : string, options = , defines the direction of the transform: forward" (time-to-frequency) or inverse (frequency-to-time)   Returns: x, y : tuple (float array, float array), real and imaginary parts of the transformed data (original x and y are changed on output) Helper functions fftPower(x, y) : Helper function that computes the power of each frequency component (in other words, Fourier amplitudes squared).   Parameters:      x : float array, real part of the Fourier amplitudes      y : float array, imaginary part of the Fourier amplitudes   Returns: power : float array of the same length as x and y , Fourier amplitudes squared fftFreq(N) : Helper function that returns the FFT sample frequencies defined in cycles per timeframe unit. For example, if the timeframe is 5m, the frequencies are in cycles/(5 minutes).   Parameters:      N : int, window length (number of points in the transformed dataset)   Returns: freq : float array of N, contains the sample frequencies (with zero at the start).
Pine Script™ library
by tbiktag
8
FunctionElementsInArrayLibrary "FunctionElementsInArray" Methods to count number of elements in arrays count_float(sample, value) Counts the number of elements equal to provided value in array.   Parameters:      sample : float array, sample data to process.      value : float value to check for equality.   Returns: int. count_int(sample, value) Counts the number of elements equal to provided value in array.   Parameters:      sample : int array, sample data to process.      value : int value to check for equality.   Returns: int. count_string(sample, value) Counts the number of elements equal to provided value in array.   Parameters:      sample : string array, sample data to process.      value : string value to check for equality.   Returns: int. count_bool(sample, value) Counts the number of elements equal to provided value in array.   Parameters:      sample : bool array, sample data to process.      value : bool value to check for equality.   Returns: int. count_color(sample, value) Counts the number of elements equal to provided value in array.   Parameters:      sample : color array, sample data to process.      value : color value to check for equality.   Returns: int. extract_indices_float(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.   Parameters:      sample : float array, sample data to process.      value : float value to check for equality.   Returns: int. extract_indices_int(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.   Parameters:      sample : int array, sample data to process.      value : int value to check for equality.   Returns: int. extract_indices_string(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.   Parameters:      sample : string array, sample data to process.      value : string value to check for equality.   Returns: int. extract_indices_bool(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.   Parameters:      sample : bool array, sample data to process.      value : bool value to check for equality.   Returns: int. extract_indices_color(sample, value) Counts the number of elements equal to provided value in array, and returns its indices.   Parameters:      sample : color array, sample data to process.      value : color value to check for equality.   Returns: int.
Pine Script™ library
by RicardoSantos
4
LinearRegressionLibraryLibrary "LinearRegressionLibrary" contains functions for fitting a regression line to the time series by means of different models, as well as functions for estimating the accuracy of the fit. Linear regression algorithms: RepeatedMedian(y, n, lastBar) applies repeated median regression (robust linear regression algorithm) to the input time series within the selected interval. Parameters: y :: float series, source time series (e.g. close) n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) Output: mSlope :: float, slope of the regression line mInter :: float, intercept of the regression line TheilSen(y, n, lastBar) applies the Theil-Sen estimator (robust linear regression algorithm) to the input time series within the selected interval. Parameters: y :: float series, source time series n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) Output: tsSlope :: float, slope of the regression line tsInter :: float, intercept of the regression line OrdinaryLeastSquares(y, n, lastBar) applies the ordinary least squares regression (non-robust) to the input time series within the selected interval. Parameters: y :: float series, source time series n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) Output: olsSlope :: float, slope of the regression line olsInter :: float, intercept of the regression line Model performance metrics: metricRMSE(y, n, lastBar, slope, intercept) returns the Root-Mean-Square Error (RMSE) of the regression. The better the model, the lower the RMSE. Parameters: y :: float series, source time series (e.g. close) n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) slope :: float, slope of the evaluated linear regression line intercept :: float, intercept of the evaluated linear regression line Output: rmse :: float, RMSE value metricMAE(y, n, lastBar, slope, intercept) returns the Mean Absolute Error (MAE) of the regression. MAE is is similar to RMSE but is less sensitive to outliers. The better the model, the lower the MAE. Parameters: y :: float series, source time series n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) slope :: float, slope of the evaluated linear regression line intercept :: float, intercept of the evaluated linear regression line Output: mae :: float, MAE value metricR2(y, n, lastBar, slope, intercept) returns the coefficient of determination (R squared) of the regression. The better the linear regression fits the data (compared to the sample mean), the closer the value of the R squared is to 1. Parameters: y :: float series, source time series n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) slope :: float, slope of the evaluated linear regression line intercept :: float, intercept of the evaluated linear regression line Output: Rsq :: float, R-sqared score Usage example: //@version=5 indicator('ExampleLinReg', overlay=true) // import the library import tbiktag/LinearRegressionLibrary/1 as linreg // define the studied interval: last 100 bars int Npoints = 100 int lastBar = bar_index int firstBar = bar_index - Npoints // apply repeated median regression to the closing price time series within the specified interval {square bracket}slope, intercept{square bracket} = linreg.RepeatedMedian(close, Npoints, lastBar) // calculate the root-mean-square error of the obtained linear fit rmse = linreg.metricRMSE(close, Npoints, lastBar, slope, intercept) // plot the line and print the RMSE value float y1 = intercept float y2 = intercept + slope * (Npoints - 1) if barstate.islast {indent} line.new(firstBar,y1, lastBar,y2) {indent} label.new(lastBar,y2,text='RMSE = '+str.format("{0,number,#.#}", rmse))
Pine Script™ library
by tbiktag
6
FunctionCompoundInterestLibrary "FunctionCompoundInterest" Method for compound interest. simple_compound(principal, rate, duration) Computes compound interest for given duration.   Parameters:      principal : float, the principal or starting value.      rate : float, the rate of interest.      duration : float, the period of growth.   Returns: float. variable_compound(principal, rates, duration) Computes variable compound interest for given duration.   Parameters:      principal : float, the principal or starting value.      rates : float array, the rates of interest.      duration : int, the period of growth.   Returns: float array. simple_compound_array(principal, rates, duration) Computes variable compound interest for given duration.   Parameters:      principal : float, the principal or starting value.      rates : float array, the rates of interest.      duration : int, the period of growth.   Returns: float array. variable_compound_array(principal, rates, duration) Computes variable compound interest for given duration.   Parameters:      principal : float, the principal or starting value.      rates : float array, the rates of interest.      duration : int, the period of growth.   Returns: float array.
Pine Script™ library
by RicardoSantos
1
FunctionBoxCoxTransformLibrary "FunctionBoxCoxTransform" Methods to compute the Box-Cox Transformer. regular(sample, lambda) Regular transform.   Parameters:      sample : float array, sample data values.      lambda : float, scaling factor.   Returns: float array. inverse(sample, lambda) Regular transform.   Parameters:      sample : float array, sample data values.      lambda : float, scaling factor.   Returns: float array.
Pine Script™ library
by RicardoSantos
2
FunctionBestFitFrequencyLibrary "FunctionBestFitFrequency" TODO: add library description here array_moving_average(sample, length, ommit_initial, fillna) Moving Average values for selected data. Parameters: sample : float array, sample data values. length : int, length to smooth the data. ommit_initial : bool, default=true, ommit values at the start of the data under the length. fillna : string, default='na', options='na', '0', 'avg' Returns: float array errors: length > sample size "Canot call array methods when id of array is na." best_fit_frequency(sample, start, end) Search a frequency range for the fairest moving average frequency. Parameters: sample : float array, sample data to based the moving averages. start : int lowest frequency. end : int highest frequency. Returns: tuple with (int frequency, float percentage)
Pine Script™ library
by RicardoSantos
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
ProbabilityLibrary "Probability" erf(value) Complementary error function Parameters: value : float, value to test. Returns: float ierf_mcgiles(value) Computes the inverse error function using the Mc Giles method, sacrifices accuracy for speed. Parameters: value : float, -1.0 >= _value >= 1.0 range, value to test. Returns: float ierf_double(value) computes the inverse error function using the Newton method with double refinement. Parameters: value : float, -1. > _value > 1. range, _value to test. Returns: float ierf(value) computes the inverse error function using the Newton method. Parameters: value : float, -1. > _value > 1. range, _value to test. Returns: float complement(probability) probability that the event will not occur. Parameters: probability : float, 0 >=_p >= 1, probability of event. Returns: float entropy_gini_impurity_single(probability) Gini Inbalance or Gini index for a given probability. Parameters: probability : float, 0>=x>=1, probability of event. Returns: float entropy_gini_impurity(events) Gini Inbalance or Gini index for a series of events. Parameters: events : float , 0>=x>=1, array with event probability's. Returns: float entropy_shannon_single(probability) Entropy information value of the probability of a single event. Parameters: probability : float, 0>=x>=1, probability value. Returns: float, value as bits of information. entropy_shannon(events) Entropy information value of a distribution of events. Parameters: events : float , 0>=x>=1, array with probability's. Returns: float inequality_chebyshev(n_stdeviations) Calculates Chebyshev Inequality. Parameters: n_stdeviations : float, positive over or equal to 1.0 Returns: float inequality_chebyshev_distribution(mean, std) Calculates Chebyshev Inequality. Parameters: mean : float, mean of a distribution std : float, standard deviation of a distribution Returns: float inequality_chebyshev_sample(data_sample) Calculates Chebyshev Inequality for a array of values. Parameters: data_sample : float , array of numbers. Returns: float intersection_of_independent_events(events) Probability that all arguments will happen when neither outcome is affected by the other (accepts 1 or more arguments) Parameters: events : float , 0 >= _p >= 1, list of event probabilities. Returns: float union_of_independent_events(events) Probability that either one of the arguments will happen when neither outcome is affected by the other (accepts 1 or more arguments) Parameters: events : float , 0 >= _p >= 1, list of event probabilities. Returns: float mass_function(sample, n_bins) Probabilities for each bin in the range of sample. Parameters: sample : float , samples to pool probabilities. n_bins : int, number of bins to split the range @return float cumulative_distribution_function(mean, stdev, value) Use the CDF to determine the probability that a random observation that is taken from the population will be less than or equal to a certain value. Or returns the area of probability for a known value in a normal distribution. Parameters: mean : float, samples to pool probabilities. stdev : float, number of bins to split the range value : float, limit at which to stop. Returns: float transition_matrix(distribution) Transition matrix for the suplied distribution. Parameters: distribution : float , array with probability distribution. ex:. Returns: float diffusion_matrix(transition_matrix, dimension, target_step) Probability of reaching target_state at target_step after starting from start_state Parameters: transition_matrix : float , "pseudo2d" probability transition matrix. dimension : int, size of the matrix dimension. target_step : number of steps to find probability. Returns: float state_at_time(transition_matrix, dimension, start_state, target_state, target_step) Probability of reaching target_state at target_step after starting from start_state Parameters: transition_matrix : float , "pseudo2d" probability transition matrix. dimension : int, size of the matrix dimension. start_state : state at which to start. target_state : state to find probability. target_step : number of steps to find probability.
Pine Script™ library
by RicardoSantos
1
MathStatisticsKernelDensityEstimationLibrary "MathStatisticsKernelDensityEstimation" (KDE) Method for Kernel Density Estimation kde(observations, kernel, bandwidth, nsteps) Parameters: observations : float array, sample data. kernel : string, the kernel to use, default='gaussian', options='uniform', 'triangle', 'epanechnikov', 'quartic', 'triweight', 'gaussian', 'cosine', 'logistic', 'sigmoid'. bandwidth : float, bandwidth to use in kernel, default=0.5, range=(0, +inf), less will smooth the data. nsteps : int, number of steps in range of distribution, default=20, this value is connected to how many line objects you can display per script. Returns: tuple with signature: (float array, float array) draw_horizontal(distribution_x, distribution_y, distribution_lines, graph_lines, graph_labels) Draw a horizontal distribution at current location on chart. Parameters: distribution_x : float array, distribution points x value. distribution_y : float array, distribution points y value. distribution_lines : line array, array to append the distribution curve lines. graph_lines : line array, array to append the graph lines. graph_labels : label array, array to append the graph labels. Returns: void, updates arrays: distribution_lines, graph_lines, graph_labels. draw_vertical(distribution_x, distribution_y, distribution_lines, graph_lines, graph_labels) Draw a vertical distribution at current location on chart. Parameters: distribution_x : float array, distribution points x value. distribution_y : float array, distribution points y value. distribution_lines : line array, array to append the distribution curve lines. graph_lines : line array, array to append the graph lines. graph_labels : label array, array to append the graph labels. Returns: void, updates arrays: distribution_lines, graph_lines, graph_labels. style_distribution(lines, horizontal, to_histogram, line_color, line_style, linewidth) Style the distribution lines. Parameters: lines : line array, distribution lines to style. horizontal : bool, default=true, if the display is horizontal(true) or vertical(false). to_histogram : bool, default=false, if graph style should be switched to histogram. line_color : color, default=na, if defined will change the color of the lines. line_style : string, defaul=na, if defined will change the line style, options=('na', line.style_solid, line.style_dotted, line.style_dashed, line.style_arrow_right, line.style_arrow_left, line.style_arrow_both) linewidth : int, default=na, if defined will change the line width. Returns: void. style_graph(lines, lines, horizontal, line_color, line_style, linewidth) Style the graph lines and labels Parameters: lines : line array, graph lines to style. lines : labels array, graph labels to style. horizontal : bool, default=true, if the display is horizontal(true) or vertical(false). line_color : color, default=na, if defined will change the color of the lines. line_style : string, defaul=na, if defined will change the line style, options=('na', line.style_solid, line.style_dotted, line.style_dashed, line.style_arrow_right, line.style_arrow_left, line.style_arrow_both) linewidth : int, default=na, if defined will change the line width. Returns: void.
Pine Script™ library
by RicardoSantos
10
MathStatisticsKernelFunctionsLibrary "MathStatisticsKernelFunctions" TODO: add library description here uniform(distance, bandwidth) Uniform kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. triangular(distance, bandwidth) Triangular kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. epanechnikov(distance, bandwidth) Epanechnikov kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. quartic(distance, bandwidth) Quartic kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. triweight(distance, bandwidth) Triweight kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. tricubic(distance, bandwidth) Tricubic kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. gaussian(distance, bandwidth) Gaussian kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. cosine(distance, bandwidth) Cosine kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. logistic(distance, bandwidth) logistic kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. sigmoid(distance, bandwidth) Sigmoid kernel. Parameters: distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float. select(kernel, distance, bandwidth) Kernel selection method. Parameters: kernel : string, kernel to select. (options="uniform", "triangle", "epanechnikov", "quartic", "triweight", "tricubic", "gaussian", "cosine", "logistic", "sigmoid") distance : float, distance to kernel origin. bandwidth : float, default=1.0, bandwidth limiter to weight the kernel. Returns: float.
Pine Script™ library
by RicardoSantos
3