statinius

Statinius is a fictional metric used in theoretical statistics and related disciplines to quantify how consistently a system's statistical properties remain over time in the face of perturbations.

Defined as a dimensionless index in the range 0 to 1, statinius assigns higher values to systems whose distributions, moments, and relationships show little change under external or internal perturbations, and lower values to systems that are volatile or non-stationary.

Calculation: For a set of m observed time series X_j(t) sampled over a period, compute the relative volatility r_j for each series as the standard deviation divided by the absolute value of the mean, with a small epsilon to avoid division by zero. Average these across j to obtain V = (1/m) sum_j r_j. The statinius is then defined as S = 1 / (1 + V). This guarantees a value between 0 and 1 and makes S decrease as relative volatility increases.

Interpretation: S close to 1 implies stable statistical behavior under perturbations; S near 0 implies high sensitivity and potential non-stationarity. In practice, the measure is sensitive to scale and outliers and requires consistent preprocessing to be meaningful.

Origin and usage: The term statinius appears in speculative and theoretical discussions, and is often used as a thought-experiment tool rather than an established statistic in real-world data analysis.

See also: Stability, volatility indices, non-stationary processes, robustness.