mcframework.stats_engine.chebyshev_required_n

mcframework.stats_engine.chebyshev_required_n(x: ndarray, ctx: StatsContext) → int

Required \(n\) to achieve Chebyshev CI half-width \(\le \varepsilon\).

With \(\delta = 1 - \text{confidence}\), the half-width is \(z\,SE = \dfrac{s}{\sqrt{n_\text{eff}\,\delta}}\) where \(z=1/\sqrt{\delta}\). Solve \(n_\text{eff} \ge \dfrac{s^2}{\varepsilon^2\,\delta}\).

Parameters:

xndarray

Input sample.

ctxStatsContext or Mapping

Must supply eps (target half-width) and may override confidence.

Returns:

int

Minimum integer \(n_\text{eff}\).

Examples

>>> chebyshev_required_n(np.array([1., 2., 3.]), {"eps": 0.5, "confidence": 0.9})
41