# Statistics > Distributions, relationships, DSP and filtering, and simulation on price series. Statistical indicators treat price as data first and chart second. Instead of reading patterns by eye, they apply standard quantitative methods: normalizing values so different markets and timeframes compare fairly, measuring how instruments move together, fitting trends with regression, and separating signal from noise with filters borrowed from engineering. The family runs from widely used basics such as z-scores and correlation to more specialized territory: trendiness and randomness measures like the Hurst exponent, John Ehlers' digital signal processing work on market cycles, and Monte Carlo simulation that turns assumptions into distributions of outcomes. Results shift with the lookback chosen, and markets are not stationary, so these tools are best read as estimates rather than guarantees. ## Normalization & distribution Transforms that put any series on a comparable scale, from z-scores and percentile ranks to min-max and sigmoid mappings, plus tools that profile how returns are actually distributed and flag outliers. - [Distribution-of-returns Profiling](https://www.luxalgo.com/library/concept/distribution-of-returns-profiling.md): 5 implementations - [Percentile Rank](https://www.luxalgo.com/library/concept/percentile-rank.md): 2 implementations - [Min-max Scaling](https://www.luxalgo.com/library/concept/min-max-scaling.md): 2 implementations - [Sigmoid/softmax Transforms](https://www.luxalgo.com/library/concept/sigmoid-softmax-transforms.md): 2 implementations - [Standard Deviation](https://www.luxalgo.com/library/concept/standard-deviation.md): 1 implementations - [Z-score](https://www.luxalgo.com/library/concept/z-score.md): 1 implementations - [Winsorization](https://www.luxalgo.com/library/concept/winsorization.md): 1 implementations - [Distribution Moments](https://www.luxalgo.com/library/concept/distribution-moments.md): 1 implementations - [Normality Testing](https://www.luxalgo.com/library/concept/normality-testing.md): 1 implementations - [Outlier Detection](https://www.luxalgo.com/library/concept/outlier-detection.md): 1 implementations ## Relationships How instruments relate, to each other and to their own past: correlation, beta and alpha, autocorrelation, and the cointegration and stationarity tests behind pairs trading. - [Correlation](https://www.luxalgo.com/library/concept/correlation.md): 10 implementations - [Beta](https://www.luxalgo.com/library/concept/beta.md): 1 implementations - [Alpha](https://www.luxalgo.com/library/concept/alpha.md): 1 implementations - [Autocorrelation](https://www.luxalgo.com/library/concept/autocorrelation.md): 1 implementations - [Lead-lag Detection](https://www.luxalgo.com/library/concept/lead-lag-detection.md): 1 implementations - [Cointegration](https://www.luxalgo.com/library/concept/cointegration.md): 1 implementations - [Pairs Trading Stack](https://www.luxalgo.com/library/concept/pairs-trading-stack.md): build pending - [Stationarity & Efficiency Tests](https://www.luxalgo.com/library/concept/stationarity-and-efficiency-tests.md): reference entry ## Complexity & memory Measures of how trending, mean-reverting, or random a market currently is, from the Hurst exponent and fractal dimension to entropy, plus change-point detection that flags when that behavior shifts. - [Hurst Exponent](https://www.luxalgo.com/library/concept/hurst-exponent.md): 1 implementations - [Fractal Dimension](https://www.luxalgo.com/library/concept/fractal-dimension.md): 1 implementations - [Entropy Measures](https://www.luxalgo.com/library/concept/entropy-measures.md): 1 implementations - [Change-point Detection](https://www.luxalgo.com/library/concept/change-point-detection.md): 1 implementations - [Market Efficiency & Regime Persistence Measures](https://www.luxalgo.com/library/concept/market-efficiency-and-regime-persistence-measures.md): reference entry ## Regression & filtering Curve fitting and smoothing methods that pull trend, cycle, and forecast structure out of noisy prices, from linear and polynomial regression to Kalman, Hodrick-Prescott, and spectral techniques. - [Linear Regression](https://www.luxalgo.com/library/concept/linear-regression.md): 8 implementations - [Polynomial Regression](https://www.luxalgo.com/library/concept/polynomial-regression.md): 4 implementations - [Quantile Regression](https://www.luxalgo.com/library/concept/quantile-regression.md): 2 implementations - [Kalman Filter](https://www.luxalgo.com/library/concept/kalman-filter.md): 1 implementations - [Hodrick-Prescott Filter](https://www.luxalgo.com/library/concept/hodrick-prescott-filter.md): 1 implementations - [Wavelet Decomposition](https://www.luxalgo.com/library/concept/wavelet-decomposition.md): 1 implementations - [FFT/spectral Analysis](https://www.luxalgo.com/library/concept/fft-spectral-analysis.md): 1 implementations - [Maximum-entropy Spectrum](https://www.luxalgo.com/library/concept/maximum-entropy-spectrum.md): 1 implementations - [Hilbert Transform](https://www.luxalgo.com/library/concept/hilbert-transform.md): 1 implementations - [Exponential Smoothing Forecasts](https://www.luxalgo.com/library/concept/exponential-smoothing-forecasts.md): 1 implementations - [LOESS Smoothing](https://www.luxalgo.com/library/concept/loess-smoothing.md): reference entry - [Signal Decomposition](https://www.luxalgo.com/library/concept/signal-decomposition.md): reference entry ## Ehlers DSP cluster John Ehlers' digital signal processing toolkit, which treats price as a noisy waveform, measures its dominant cycle, and adapts indicator parameters to what it finds. - [Dominant Cycle Measurement](https://www.luxalgo.com/library/concept/dominant-cycle-measurement.md): 3 implementations - [Sinewave Indicator](https://www.luxalgo.com/library/concept/sinewave-indicator.md): 2 implementations - [Roofing Filter](https://www.luxalgo.com/library/concept/roofing-filter.md): 1 implementations - [Decycler](https://www.luxalgo.com/library/concept/decycler.md): 1 implementations - [Even-better Sinewave](https://www.luxalgo.com/library/concept/even-better-sinewave.md): 1 implementations - [Adaptive-parameter Technique](https://www.luxalgo.com/library/concept/adaptive-parameter-technique.md): 1 implementations - [Autocorrelation Periodogram](https://www.luxalgo.com/library/concept/autocorrelation-periodogram.md): reference entry ## Simulation Methods that turn assumptions into ranges of outcomes: Monte Carlo price paths, resampling tests on historical data, and probability cones that frame plausible futures instead of single forecasts. - [Monte Carlo Price Paths](https://www.luxalgo.com/library/concept/monte-carlo-price-paths.md): 5 implementations - [Probability Cones](https://www.luxalgo.com/library/concept/probability-cones.md): 5 implementations - [Resampling Tests](https://www.luxalgo.com/library/concept/resampling-tests.md): 2 implementations - [Random-entry Baselines](https://www.luxalgo.com/library/concept/random-entry-baselines.md): build pending --- Source: https://www.luxalgo.com/library/family/statistics/ (LuxAlgo Library). Free to use with attribution: https://www.luxalgo.com/library/license/