Flexible Distribution Fit Panel

A plain mean/standard-deviation summary of returns assumes the distribution is symmetric. Real return distributions usually are not - they skew, and a normal-distribution summary throws that information away. This panel instead fits Azzalini's skew-normal family, which adds a third parameter (shape/skew) on top of location and scale, to the trailing window of returns. The fit method is named explicitly because it is a deliberate simplification: the textbook way to fit a skew-normal is maximum likelihood, which needs iterative numerical optimisation - MQL4 has no general-purpose solver for that. The method-of-moments estimator used here is closed-form instead: it matches the sample's mean, variance and skewness exactly to the three skew-normal parameters (xi, omega, alpha) via Azzalini's published algebraic relations, no iteration required. This is a standard, documented alternative to MLE for this family, not an ad-hoc shortcut - it is exact for the three moments it targets, though not identical to a full MLE fit on any other measure. Sample skewness has a hard mathematical ceiling for what any skew-normal distribution can represent (|skewness| < ~0.9953, regardless of alpha); when a window's own skewness exceeds that, the panel clamps to the boundary and says so plainly rather than producing an undefined or nonsensical fit. Notes and limitations - The fit is method-of-moments, not maximum likelihood - it matches mean/variance/skewness exactly but is not guaranteed to be the single "best" fit by every other criterion (e.g. it does not directly target kurtosis or tail probability at all). - Skew-normal itself has a hard skewness ceiling (~0.9953 in magnitude); a window whose sample skewness exceeds that gets clamped to the boundary, and the panel flags this explicitly rather than hiding it. - The panel updates once per completed bar, not intrabar, so the displayed fit describes the settled distribution of completed bars only. - This describes the shape of RETURNS over the lookback window, not a forecast - it says what the recent distribution has looked like, not what tomorrow's return will be.

Indicator · MT4 · v1.0 · Free

Tags: Trailing Stop & Break-even · MT4 Indicator · MQL4 Source Code

MetaTrader 4 & 5 indicators · PolyMaria