EGDF (Entropic Global Distribution Function)

Every statistical quality calculation — capability indices, control limits, tolerance intervals, process comparisons — depends on knowing the distribution of your data. Traditional methods force you to choose a distribution family first (normal, lognormal, Weibull, etc.), then fit parameters. If you choose wrong, every downstream calculation is biased.

The EGDF eliminates the distribution selection step entirely. It learns the distribution shape from the data itself, producing a continuous CDF that can be used anywhere a parametric CDF would be used — but without the risk of model misspecification.

This is particularly important for automated quality systems where an engineer is not manually verifying each dataset's distribution. An API call to EGDF produces a reliable distribution estimate regardless of what shape the data takes.

The EGDF is the core of EntropyStat's analytical engine. Built on over 40 years of mathematical research at the Czech Academy of Sciences, it uses gnostic algebra — a deterministic optimization framework based on entropy principles and error geometry — to construct distribution functions.

Key properties that distinguish EGDF from parametric fitting and kernel density estimation: it produces the same result every time (deterministic, no random seeds), it is inherently robust to outliers because it uses supremum-based optimization rather than least-squares, and it works reliably with as few as 5–8 data points because it does not need to estimate parametric distribution parameters.

The EGDF supports both additive form (for data spanning positive and negative values) and multiplicative form (for strictly positive data with proportional variation). The Scale parameter controls smoothness and is auto-optimized using the Kolmogorov-Smirnov test. The result is a continuous CDF with well-defined bounds, from which EntropyStat derives all downstream metrics: percentiles, capability indices, tolerance intervals, and control limits.