Module stats 

Standard normal distribution helpers for Wald inference (no external deps).

Accurate to near machine precision, so p-values and critical values match SciPy (and therefore Python DoubleML) to ~1e-14.

Functions

erfc

Complementary error function erfc(x) = 1 − erf(x).

norm_cdf

Standard normal CDF Φ(x).

norm_ppf

Standard normal quantile Φ⁻¹(p) for 0 < p < 1: Acklam’s rational approximation followed by one Halley refinement step.

norm_sf

Standard normal survival function 1 − Φ(x), accurate in the upper tail.