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https://github.com/mihakralj/QuanTAlib.git
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Refactor documentation links in numerics, oscillators, reversals, and statistics modules to use relative paths; update Bias class to handle division by zero more robustly; remove obsolete CUMMEAN Pine script; enhance trend indicators documentation; add Visual Studio Code workspace configuration.
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Miha Kralj
+30
-31
@@ -6,34 +6,33 @@ Statistical tools applied to price and returns. These indicators quantify relati
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| Indicator | Full Name | Description |
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| :--- | :--- | :--- |
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| [ACF](/lib/statistics/acf/Acf.md) | Autocorrelation Function | Correlation of time series with lagged copy. For ARMA model identification. |
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| [BETA](/lib/statistics/beta/Beta.md) | Beta Coefficient | Asset volatility relative to market. β=1 means market-matched risk. |
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| [BIAS](/lib/statistics/bias/Bias.md) | Bias | Percentage deviation from moving average. Measures overextension. |
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| [CMA](/lib/statistics/cma/Cma.md) | Cumulative Moving Average | Running average of all values. Welford's algorithm. No window. |
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| [COINTEGRATION](/lib/statistics/cointegration/Cointegration.md) | Cointegration | Tests if series share long-term equilibrium. Pairs trading foundation. |
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| [CORRELATION](/lib/statistics/correlation/Correlation.md) | Correlation | Linear relationship between two variables. Range: -1 to +1. |
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| [COVARIANCE](/lib/statistics/covariance/Covariance.md) | Covariance | Joint variability of two random variables. Building block for β. |
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| [CUMMEAN](/lib/statistics/cummean/Cummean.md) | Cumulative Mean | Cumulative mean from series start. Ignores NaN values. |
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| [ENTROPY](/lib/statistics/entropy/Entropy.md) | Shannon Entropy | Measures uncertainty/randomness. Higher entropy = less predictable. |
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| [GEOMEAN](/lib/statistics/geomean/Geomean.md) | Geometric Mean | nth root of product. Use for growth rates and ratios. |
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| [GRANGER](/lib/statistics/granger/Granger.md) | Granger Causality | Tests if one series helps predict another. Not true causality. |
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| [HARMEAN](/lib/statistics/harmean/Harmean.md) | Harmonic Mean | Reciprocal of arithmetic mean of reciprocals. For rates/ratios. |
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| [HURST](/lib/statistics/hurst/Hurst.md) | Hurst Exponent | Long-term memory. H>0.5: trending. H<0.5: mean-reverting. |
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| [IQR](/lib/statistics/iqr/Iqr.md) | Interquartile Range | P75 - P25. Robust dispersion measure. |
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| [JB](/lib/statistics/jb/Jb.md) | Jarque-Bera Test | Normality test using skewness and kurtosis. |
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| [KENDALL](/lib/statistics/kendall/Kendall.md) | Kendall Rank Correlation | Ordinal association. Robust to outliers. |
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| [KURTOSIS](/lib/statistics/kurtosis/Kurtosis.md) | Kurtosis | Tail heaviness. High kurtosis = fat tails = more extreme events. |
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| [LINREG](/lib/statistics/linreg/LinReg.md) | Linear Regression | Least squares fit. Outputs slope, intercept, R². |
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| [MEDIAN](/lib/statistics/median/Median.md) | Median | Middle value in sorted window. Robust to outliers. |
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| [MODE](/lib/statistics/mode/Mode.md) | Mode | Most frequent value. Use for categorical or discrete data. |
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| [PACF](/lib/statistics/pacf/Pacf.md) | Partial Autocorrelation Function | Direct correlation at lag k after removing intermediate effects. For AR model identification. |
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| [PERCENTILE](/lib/statistics/percentile/Percentile.md) | Percentile | Value below which given percentage of observations fall. |
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| [QUANTILE](/lib/statistics/quantile/Quantile.md) | Quantile | Divides distribution into equal probability intervals. |
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| [SKEW](/lib/statistics/skew/Skew.md) | Skewness | Distribution asymmetry. Positive: right tail. Negative: left tail. |
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| [SPEARMAN](/lib/statistics/spearman/Spearman.md) | Spearman Rank Correlation | Pearson on ranks. Measures monotonic relationship. |
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| [STDDEV](/lib/statistics/stddev/StdDev.md) | Standard Deviation | Square root of variance. Same units as data. |
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| [SUM](/lib/statistics/sum/Sum.md) | Rolling Sum | Kahan-Babuška summation. Numerically stable. |
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| [THEIL](/lib/statistics/theil/Theil.md) | Theil Index | Inequality measure. Decomposable into within/between group. |
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| [VARIANCE](/lib/statistics/variance/Variance.md) | Variance | Average squared deviation from mean. Units are squared. |
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| [ZSCORE](/lib/statistics/zscore/Zscore.md) | Z-Score | Standard deviations from mean. Normalizes different scales. |
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| [ZTEST](/lib/statistics/ztest/Ztest.md) | Z-Test | Hypothesis test comparing sample mean to population mean. |
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| [ACF](acf/Acf.md) | Autocorrelation Function | Correlation of time series with lagged copy. For ARMA model identification. |
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| [BETA](beta/Beta.md) | Beta Coefficient | Asset volatility relative to market. β=1 means market-matched risk. |
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| [BIAS](bias/Bias.md) | Bias | Percentage deviation from moving average. Measures overextension. |
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| [CMA](cma/Cma.md) | Cumulative Moving Average | Running average of all values. Welford's algorithm. No window. |
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| [COINTEGRATION](cointegration/Cointegration.md) | Cointegration | Tests if series share long-term equilibrium. Pairs trading foundation. |
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| [CORRELATION](correlation/Correlation.md) | Correlation | Linear relationship between two variables. Range: -1 to +1. |
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| [COVARIANCE](covariance/Covariance.md) | Covariance | Joint variability of two random variables. Building block for β. |
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| [ENTROPY](entropy/Entropy.md) | Shannon Entropy | Measures uncertainty/randomness. Higher entropy = less predictable. |
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| [GEOMEAN](geomean/Geomean.md) | Geometric Mean | nth root of product. Use for growth rates and ratios. |
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| [GRANGER](granger/Granger.md) | Granger Causality | Tests if one series helps predict another. Not true causality. |
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| [HARMEAN](harmean/Harmean.md) | Harmonic Mean | Reciprocal of arithmetic mean of reciprocals. For rates/ratios. |
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| [HURST](hurst/Hurst.md) | Hurst Exponent | Long-term memory. H>0.5: trending. H<0.5: mean-reverting. |
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| [IQR](iqr/Iqr.md) | Interquartile Range | P75 - P25. Robust dispersion measure. |
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| [JB](jb/Jb.md) | Jarque-Bera Test | Normality test using skewness and kurtosis. |
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| [KENDALL](kendall/Kendall.md) | Kendall Rank Correlation | Ordinal association. Robust to outliers. |
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| [KURTOSIS](kurtosis/Kurtosis.md) | Kurtosis | Tail heaviness. High kurtosis = fat tails = more extreme events. |
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| [LINREG](linreg/LinReg.md) | Linear Regression | Least squares fit. Outputs slope, intercept, R². |
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| [MEDIAN](median/Median.md) | Median | Middle value in sorted window. Robust to outliers. |
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| [MODE](mode/Mode.md) | Mode | Most frequent value. Use for categorical or discrete data. |
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| [PACF](pacf/Pacf.md) | Partial Autocorrelation Function | Direct correlation at lag k after removing intermediate effects. For AR model identification. |
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| [PERCENTILE](percentile/Percentile.md) | Percentile | Value below which given percentage of observations fall. |
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| [QUANTILE](quantile/Quantile.md) | Quantile | Divides distribution into equal probability intervals. |
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| [SKEW](skew/Skew.md) | Skewness | Distribution asymmetry. Positive: right tail. Negative: left tail. |
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| [SPEARMAN](spearman/Spearman.md) | Spearman Rank Correlation | Pearson on ranks. Measures monotonic relationship. |
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| [STDDEV](stddev/StdDev.md) | Standard Deviation | Square root of variance. Same units as data. |
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| [SUM](sum/Sum.md) | Rolling Sum | Kahan-Babuška summation. Numerically stable. |
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| [THEIL](theil/Theil.md) | Theil Index | Inequality measure. Decomposable into within/between group. |
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| [VARIANCE](variance/Variance.md) | Variance | Average squared deviation from mean. Units are squared. |
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| [ZSCORE](zscore/Zscore.md) | Z-Score | Standard deviations from mean. Normalizes different scales. |
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| [ZTEST](ztest/Ztest.md) | Z-Test | Hypothesis test comparing sample mean to population mean. |
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@@ -43,6 +43,7 @@ public sealed class Bias : AbstractBase
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private State _p_state;
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private const int ResyncInterval = 1000;
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private const double Epsilon = 1e-10;
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/// <summary>
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/// Creates Bias with specified period.
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@@ -138,7 +139,7 @@ public sealed class Bias : AbstractBase
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// Calculate final Bias
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double sma = _state.Sum / _buffer.Count;
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double bias = sma != 0 ? (_state.LastInput - sma) / sma : 0;
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double bias = Math.Abs(sma) > Epsilon ? (_state.LastInput - sma) / sma : 0;
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Last = new TValue(DateTime.MinValue, bias);
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_p_state = _state;
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}
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@@ -202,7 +203,7 @@ public sealed class Bias : AbstractBase
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// Calculate Bias: (Price - SMA) / SMA
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double sma = _state.Sum / _buffer.Count;
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double bias = sma != 0 ? (_state.LastInput - sma) / sma : 0;
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double bias = Math.Abs(sma) > Epsilon ? (_state.LastInput - sma) / sma : 0;
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Last = new TValue(input.Time, bias);
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PubEvent(Last, isNew);
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@@ -327,7 +328,7 @@ public sealed class Bias : AbstractBase
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double n = i + 1;
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double sma = sum / n;
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output[i] = sma != 0 ? (val - sma) / sma : 0;
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output[i] = Math.Abs(sma) > Epsilon ? (val - sma) / sma : 0;
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}
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// Main phase with sliding window
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@@ -354,7 +355,7 @@ public sealed class Bias : AbstractBase
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}
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double sma = sum / period;
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output[i] = sma != 0 ? (val - sma) / sma : 0;
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output[i] = Math.Abs(sma) > Epsilon ? (val - sma) / sma : 0;
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// Periodic resync for long sequences
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tickCount++;
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@@ -1,27 +0,0 @@
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// The MIT License (MIT)
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// © mihakralj
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//@version=6
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indicator("Cumulative Mean (CUMMEAN)", "CUMMEAN", overlay=false, precision=8)
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//@function Calculates the cumulative arithmetic mean (average) of a series from the start of the data.
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//@doc https://github.com/mihakralj/pinescript/blob/main/indicators/statistics/cummean.md
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//@param src series float Input data series.
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//@returns series float The cumulative mean of the series, or na if all data so far is na.
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cummean(series float src) =>
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var float cumulative_sum = 0.0
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var int valid_data_count = 0
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if not na(src)
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cumulative_sum += src
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valid_data_count += 1
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valid_data_count > 0 ? cumulative_sum / valid_data_count : na
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// ---------- Main loop ----------
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// Inputs
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i_source = input.source(close, "Source")
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// Calculation
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cummean_value = cummean(i_source)
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// Plot
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plot(cummean_value, "CumMean", color=color.new(color.blue, 0, color=color.yellow, linewidth=2), linewidth=2)
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