mapie.metrics.kuiper_cdf

mapie.metrics.kuiper_cdf(x: float) → float

Compute the Kuiper cumulative distribution function (CDF) for the float x. This is interpreted as the CDF of the range of the standard Brownian motion over the unit interval [0, 1]. The function is approximated by its power series, truncated so as to hit machine precision error.

Parameters

xfloat

The float x to compute the cumulative distribution function.

Returns

float

The Kuiper cumulative distribution function.

References

Tygert M. Calibration of P-values for calibration and for deviation of a subpopulation from the full population. arXiv preprint arXiv:2202.00100. 2022 Jan 31.

William Feller. The Asymptotic Distribution of the Range of Sums of Independent Random Variables. Ann. Math. Statist. 22 (3) 427 - 432 September, 1951.