mcframework.stats_engine.ci_mean_chebyshev

mcframework.stats_engine.ci_mean_chebyshev(x: ndarray, ctx: StatsContext) → dict[str, float | str] | None

Distribution-free CI for \(\mathbb{E}[X]\) via Chebyshev’s inequality.

For \(\delta = 1 - \text{confidence}\), choose \(z=1/\sqrt{\delta}\) so that

\[\Pr\!\left(\,|\bar X - \mu| \ge z\,SE\,\right) \le \delta, \qquad SE = \frac{s}{\sqrt{n_\text{eff}}}.\]

Parameters:

xndarray

Input sample.

ctxStatsContext or Mapping

Requires n and may specify confidence.

Returns:

dict[str, float | str] or None

Mapping with keys confidence, method, low, and high, or None if \(n_\text{eff} < 2\).