kuiper_false_positive_probability

astropy.stats.kuiper_false_positive_probability(D, N)[source]

Compute the false positive probability for the Kuiper statistic.

Uses the set of four formulas described in Paltani 2004; they report the resulting function never underestimates the false positive probability but can be a bit high in the N=40..50 range. (They quote a factor 1.5 at the 1e-7 level.)

Parameters:
D : float

The Kuiper test score.

N : float

The effective sample size.

Returns:
fpp : float

The probability of a score this large arising from the null hypothesis.

Notes

Eq 7 of Paltani 2004 appears to incorrectly quote the original formula (Stephens 1965). This function implements the original formula, as it produces a result closer to Monte Carlo simulations.

References

[1]Paltani, S., “Searching for periods in X-ray observations using Kuiper’s test. Application to the ROSAT PSPC archive”, Astronomy and Astrophysics, v.240, p.789-790, 2004.
[2]Stephens, M. A., “The goodness-of-fit statistic VN: distribution and significance points”, Biometrika, v.52, p.309, 1965.