Approximate Critical Values for Kolmogorov-Smirnov's D

Computes the critical value for Kolmogorov-Smirnov's \(D_n\), for sample sizes \(n \ge 10\) and confidence level 95%.

KSd(n)

Details

Based on tables values given in the reference below. For \(n\le 80\) uses interpolations from exact values, elsewhere uses asymptotic approximation.

Arguments

n

the sample size, n >= 10.

Value

The critical value for D (two-sided) for significance level 0.05 (or confidence level 95%).

References

Peter J. Bickel and Kjell A. Doksum (1977), Mathematical Statistics: Basic Ideas and Selected Topics. Holden Day. Section 9.6 and table IX.

Author

Kjetil Halvorsen and Martin Maechler

See also

Is used from ecdf.ksCI.

Examples

KSd(90)
#> [1] 0.1411873
KSd(1:9)# now works
#> [1] 0.97500 0.84189 0.70760 0.62394 0.56328 0.51926 0.48342 0.45427 0.43001

op <- par(mfrow=c(2,1))
  plot(KSd, 10, 150)# nice
  abline(v = c(75,85), col = "gray")
  plot(KSd, 79, 81, n = 1001)# *very* tiny discontinuity at 80

par(op)