ks_c_cdf: Exact-KS-FFT Complementary CDF from Pre-computed Boundaries

In KSgeneral: Computing P-Values of the One-Sample K-S Test and the Two-Sample K-S and Kuiper Tests for (Dis)Continuous Null Distribution

Exact-KS-FFT Complementary CDF from Pre-computed Boundaries

Description

Computes the complementary cumulative distribution function used by the one-sample Exact-KS-FFT method from pre-computed lower and upper boundary vectors, without using an intermediate file.

Usage

ks_c_cdf(n, A, B)

Arguments

n	A positive integer giving the sample size.
A	A numeric vector of length n containing the lower boundary values A_i, in nondecreasing order, with values in [0,1].
B	A numeric vector of length n containing the upper boundary values B_i, in nondecreasing order, with values in [0,1].

Details

The function evaluates the Exact-KS-FFT boundary-crossing calculation directly from the vectors A_i and B_i. These vectors define the rectangular region for the uniform order statistics,

A_i \le U_{(i)} \le B_i, \qquad i=1,\ldots,n.

It returns the complementary probability

1 - P(A_i \le U_{(i)} \le B_i,\ i=1,\ldots,n).

The boundary values can be constructed as in Steps 1 and 2 of the Exact-KS-FFT method of Dimitrova, Kaishev and Tan (2020). For the standard two-sided one-sample KS problem with a continuous null distribution and fixed q, one may use

A_i = \max(0, i/n-q), \qquad B_i = \min(1, (i-1)/n+q).

This interface replaces the historical package-internal mechanism that wrote the boundary vectors to ‘Boundary_Crossing_Time.txt’ before calling C++. The vectors are now passed directly to the C++ implementation.

Value

A numeric value giving the complementary probability associated with the specified boundary vectors. For boundaries corresponding to a one-sample KS statistic at threshold q, this is the Exact-KS-FFT p-value P(D_n \ge q).

References

Dimitrina S. Dimitrova, Vladimir K. Kaishev, Senren Tan. (2020) "Computing the Kolmogorov-Smirnov Distribution When the Underlying CDF is Purely Discrete, Mixed or Continuous". Journal of Statistical Software, 95(10), 1–42. doi:10.18637/jss.v095.i10.

Moscovich A., Nadler B. (2017). "Fast Calculation of Boundary Crossing Probabilities for Poisson Processes". Statistics and Probability Letters, 123, 177–182.

Examples

## Two-sided one-sample KS boundaries for a continuous null distribution
n <- 10
q <- 0.1
A <- pmax(0, (1:n) / n - q)
B <- pmin(1, ((1:n) - 1) / n + q)

ks_c_cdf(n, A, B)

KSgeneral documentation built on Aug. 23, 2026, 9:07 a.m.