# Distribution Moments Computes the shape of a rolling return distribution (mean, variance, standard deviation, skewness, and kurtosis) over 252 bars of log returns, plotting a chosen moment (skewness by default) while a dashboard reports all of them with tail reads. Alerts fire when skewness crosses ±0.5 or raw kurtosis clears 3, flagging asymmetry and fat tails for quantitative traders. - Indicator in the LuxAlgo Library, by LuxAlgo, published May 19, 2026. - Access: free. - Concepts: [Distribution Moments](https://www.luxalgo.com/library/concept/distribution-moments/) (primary) - Open on Vela: https://vela.luxalgo.com/chart?pineScriptCodeId=n357teg2h6jahf10gju9rp0n - Page: https://www.luxalgo.com/library/indicator/distribution-moments/ **Distribution Moments** turns a rolling window of returns into the numbers that describe its shape (mean, variance and standard deviation, skewness, and kurtosis), plotting one of them in the pane while a dashboard reports them all. Built as the reference implementation of [distribution moments](https://www.luxalgo.com/library/concept/distribution-moments/) for charts, it computes log returns of the close over 252 bars by default, plots skewness against a dotted reference level, and fires alerts when asymmetry or tail weight crosses your thresholds. ## How to Trade the Distribution Moments? - **Skewness at or below -0.5**: the dashboard flags Left Tail (recent surprises lean downside); readings at or above +0.5 flag Right Tail. - **Kurtosis above 3**: heavier tails than the normal benchmark, an argument for wider stops and smaller size. - **Std Dev row**: per-bar return dispersion, the scale the shape numbers are standardized by. - **Regime drift**: watch the plotted moment's trend rather than single prints. Return shape tells you how far to trust the other [statistical tools](https://www.luxalgo.com/library/family/statistics/). ## Distribution Moments Settings - **Source** (default close): series the return sample is built from. - **Return Type** (default Log): log returns are standard; Simple for comparison. - **Window Length** (default 252): returns in the rolling sample. Higher moments want hundreds of observations. - **Plotted Moment** (default Skewness): which of the five series the pane displays. - **Kurtosis Convention** (default Raw (Normal = 3)): Raw benchmarks normal at 3; Excess subtracts that 3. - **Skewness Alert Threshold** (default 0.5): absolute level for the tail alerts and dashboard read. - **Kurtosis Alert Threshold** (default 3.0): raw kurtosis level marking fat tails. - **Show Dashboard** (default enabled) and **Gradient Fill** (default enabled) round out the pane. ## Frequently Asked Questions ### Why not just watch standard deviation? Because it is only the second moment. [Standard Deviation](https://www.luxalgo.com/library/indicator/standard-deviation/) measures dispersion but says nothing about which side the outliers favor or how heavy the tails run. Identical volatility can hide very different downside risk. ### Why did a reading jump with no obvious news? The third and fourth moments raise each deviation to the 3rd and 4th power, handing a single extreme bar outsized influence. A reading can lurch when an old outlier drops out of the 252-bar sample, an artifact of the window, not fresh information. ### Should I use raw or excess kurtosis? They differ by exactly 3, nothing more: Raw benchmarks the normal distribution at 3, Excess at 0. Pick whichever convention your other sources use. The alerts evaluate raw kurtosis either way. ## Related indicators - [Reversal Probability Zone & Levels](https://www.luxalgo.com/library/indicator/reversal-probability-zone-levels/) (Percentile Rank): markdown at https://www.luxalgo.com/library/indicator/reversal-probability-zone-levels.md - [Consecutive Candle Streak Analysis](https://www.luxalgo.com/library/indicator/consecutive-candle-streak-analysis/) (Distribution-of-returns Profiling): markdown at https://www.luxalgo.com/library/indicator/consecutive-candle-streak-analysis.md - [Probability Grid](https://www.luxalgo.com/library/indicator/probability-grid/) (Distribution-of-returns Profiling): markdown at https://www.luxalgo.com/library/indicator/probability-grid.md - [Change-Point Detection (CUSUM)](https://www.luxalgo.com/library/indicator/change-point-detection-cusum/) (Outlier Detection): markdown at https://www.luxalgo.com/library/indicator/change-point-detection-cusum.md - [Standardized Cumulative Deltas](https://www.luxalgo.com/library/indicator/standardized-cumulative-deltas/) (Z-score): markdown at https://www.luxalgo.com/library/indicator/standardized-cumulative-deltas.md - [Sigmoid Transition Trailing Stop](https://www.luxalgo.com/library/indicator/sigmoid-transition-trailing-stop/) (Sigmoid/softmax Transforms): markdown at https://www.luxalgo.com/library/indicator/sigmoid-transition-trailing-stop.md - [ATR Exceedance Probability Model](https://www.luxalgo.com/library/indicator/atr-exceedance-probability-model/) (Distribution-of-returns Profiling): markdown at https://www.luxalgo.com/library/indicator/atr-exceedance-probability-model.md - [Percentile Nearest Rank Using Arrays](https://www.luxalgo.com/library/indicator/percentile-nearest-rank-using-arrays/) (Percentile Rank): markdown at https://www.luxalgo.com/library/indicator/percentile-nearest-rank-using-arrays.md --- Source: https://www.luxalgo.com/library/indicator/distribution-moments/ (LuxAlgo Library). Free to use with attribution: https://www.luxalgo.com/library/license/