R Under development (unstable) (2023-09-19 r85175) -- "Unsuffered Consequences"
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> set.seed(290875)
> B <- 1e5
> 
> ### note: psmirnov(, z = NULL) uses stats:::C_pSmirnov2x, z = something
> ### trigger Schröer-Trenkler algo
> all.equal(psmirnov(1:999/1000, sizes = c(10, 20), z = 1:30), 
+           psmirnov(1:999/1000, sizes = c(10, 20)))
[1] TRUE
> 
> ### examples by Schröer & Trenkler (1995) without ties
> all.equal(psmirnov(3 / 7, sizes = c(7, 5), z = 1:12), 
+           psmirnov(3 / 7, sizes = c(7, 5)))
[1] TRUE
> 
> all.equal(psmirnov(sizes = c(m = 3, n = 4), q = 1/2, z = 1:7, lower.tail = FALSE),
+           psmirnov(sizes = c(m = 3, n = 4), q = 1/2, lower.tail = FALSE))
[1] TRUE
> psmirnov(sizes = c(m = 3, n = 4), q = 1/6, z = 1:7, lower.tail = FALSE, alternative = "greater")
[1] 0.8
> psmirnov(sizes = c(m = 4, n = 3), q = 1/2, z = 1:7, lower.tail = FALSE, alternative = "greater")
[1] 0.3428571
> 
> all.equal(psmirnov(sizes = c(m = 5, n = 7), q = 3 / 7, z = 1:12, lower.tail = FALSE),
+           psmirnov(sizes = c(m = 5, n = 7), q = 3 / 7, z = 1:12, lower.tail = FALSE))
[1] TRUE
> 
> all.equal(psmirnov(sizes = c(m = 300, n = 520), q = 1/8, z = 1:820, lower.tail = FALSE),
+           psmirnov(sizes = c(m = 300, n = 520), q = 1/8, lower.tail = FALSE))
[1] TRUE
> psmirnov(z = round(rnorm(820)), sizes = c(m = 300, n = 520), 
+          q = 1/8, lower.tail = FALSE)
[1] 0.00038641
> 
> ### tied example by Schröer & Trenkler (1995)
> x <- c(1, 2, 2, 3, 3, 1, 2, 3, 3, 4, 5, 6)
> psmirnov(z = x, sizes = c(m = 5, n = 7), q = 3 / 7, lower.tail = FALSE)
[1] 0.2424242
> psmirnov(z = x, sizes = c(m = 5, n = 7), q = 3 / 7, lower.tail = FALSE, 
+          exact = FALSE, simulate = TRUE, B = B)
[1] 0.24239
> psmirnov(z = x, sizes = c(m = 5, n = 7), q = 3 / 7, lower.tail = FALSE, alternative = "greater")
[1] 0.1780303
> psmirnov(z = x, sizes = c(m = 5, n = 7), q = 3 / 7, lower.tail = FALSE, alternative = "greater",
+          exact = FALSE, simulate = TRUE, B = B)
[1] 0.17847
> psmirnov(z = x, sizes = c(m = 5, n = 7), q = 3 / 7, lower.tail = TRUE, alternative = "greater")
[1] 0.8219697
> psmirnov(z = x, sizes = c(m = 5, n = 7), q = 3 / 7, lower.tail = TRUE, alternative = "greater",
+          exact = FALSE, simulate = TRUE, B = B)
[1] 0.8232
> 
> ### check quantiles
> ### Kim & Jennrich (1973) in Selected Tables in Mathematical Statistics, Vol 1
> ### (ed. Harter) Institute of Mathematical Statistics, page 129
> all.equal(qsmirnov(1 - .05, sizes = c(m = 8, n = 6)) * 8 * 6, 34)
[1] TRUE
> all.equal(qsmirnov(1 - .01, sizes = c(m = 8, n = 6)) * 8 * 6, 40)
[1] TRUE
> all.equal(qsmirnov(1 - .001, sizes = c(m = 8, n = 6)) * 8 * 6, 48)
[1] TRUE
> all.equal(qsmirnov(1 - .05, sizes = c(m = 14, n = 10)) * 140, 74)
[1] TRUE
> all.equal(qsmirnov(1 - .01, sizes = c(m = 14, n = 10)) * 140, 90)
[1] TRUE
> all.equal(qsmirnov(1 - .001, sizes = c(m = 14, n = 10)) * 140, 106)
[1] TRUE
> ### Schröer algo
> all.equal(qsmirnov(1 - .05, sizes = c(m = 8, n = 6), z = 1:14) * 8 * 6, 34)
[1] TRUE
> all.equal(qsmirnov(1 - .01, sizes = c(m = 8, n = 6), z = 1:14) * 8 * 6, 40)
[1] TRUE
> all.equal(qsmirnov(1 - .001, sizes = c(m = 8, n = 6), z = 1:14) * 8 * 6, 48)
[1] TRUE
> all.equal(qsmirnov(1 - .05, sizes = c(m = 14, n = 10), z = 1:24) * 140, 74)
[1] TRUE
> all.equal(qsmirnov(1 - .01, sizes = c(m = 14, n = 10), z = 1:24) * 140, 90)
[1] TRUE
> all.equal(qsmirnov(1 - .001, sizes = c(m = 14, n = 10), z = 1:24) * 140, 106)
[1] TRUE
> ### Monte Carlo
> all.equal(qsmirnov(1 - .05, sizes = c(m = 8, n = 6), z = 1:14, exact = FALSE, simulate = TRUE, B = B) * 8 * 6, 34)
[1] TRUE
> all.equal(qsmirnov(1 - .01, sizes = c(m = 8, n = 6), z = 1:14, exact = FALSE, simulate = TRUE, B = B) * 8 * 6, 40)
[1] TRUE
> all.equal(qsmirnov(1 - .001, sizes = c(m = 8, n = 6), z = 1:14, exact = FALSE, simulate = TRUE, B = B) * 8 * 6, 48)
[1] TRUE
> all.equal(qsmirnov(1 - .05, sizes = c(m = 14, n = 10), z = 1:24, exact = FALSE, simulate = TRUE, B = B) * 140, 74)
[1] TRUE
> all.equal(qsmirnov(1 - .01, sizes = c(m = 14, n = 10), z = 1:24, exact = FALSE, simulate = TRUE, B = B) * 140, 90)
[1] TRUE
> all.equal(qsmirnov(1 - .001, sizes = c(m = 14, n = 10), z = 1:24, exact = FALSE, simulate = TRUE, B = B) * 140, 106)
[1] TRUE
> 
> ### without ties
> q <- qsmirnov(1:9/10, sizes = c(5, 7))
> p <- psmirnov(q, sizes = c(5, 7))
> all.equal(qsmirnov(p, sizes = c(5, 7)), q)
[1] TRUE
> 
> ### with ties
> obs <- c(1, 2, 2, 3, 3, 1, 2, 3, 3, 4, 5, 6)
> q <- qsmirnov(1:9/10, sizes = c(5, 7), z = obs)
> p <- psmirnov(q, sizes = c(5, 7), z = obs)
> all.equal(qsmirnov(p, sizes = c(5, 7), z = obs), q)
[1] TRUE
> 
> ### without ties
> q <- qsmirnov(1:9/10, sizes = c(5, 7), alternative = "greater")
> p <- psmirnov(q, sizes = c(5, 7), alternative = "greater")
> all.equal(qsmirnov(p, sizes = c(5, 7), alternative = "greater"), q)
[1] TRUE
> 
> ### with ties
> obs <- c(1, 2, 2, 3, 3, 1, 2, 3, 3, 4, 5, 6)
> q <- qsmirnov(1:9/10, sizes = c(5, 7), z = obs, alternative = "greater")
> p <- psmirnov(q, sizes = c(5, 7), z = obs, alternative = "greater")
> all.equal(qsmirnov(p, sizes = c(5, 7), z = obs, alternative = "greater"), q)
[1] TRUE
> 
> ## PR#18582
> ## <https://bugs.r-project.org/show_bug.cgi?id=18582>
> ## KS.Test with specific data contradicts itself
> ## See explanations in the PR: the permutation distributions of the
> ## one-sided statistics can be different in the case of ties.
> ## The C code for the exact and MC simulations only implements one-sided
> ## D_{xy}^+ ("greater"); the R code now knows that D_{xy}^- = D_{yx}^+
> ## ("less").
> 
> x <- scan(text="4.7 5.5 6.7 7.1")
Read 4 items
> y <- scan(text="2.3 3.4 4.0 4.3 4.3 4.3 4.5 5.0")
Read 8 items
> all.equal(ks.test(x, y, alternative = "less")$p.value,
+           ks.test(y, x, alternative = "greater")$p.value)
[1] TRUE
> all.equal(ks.test(y, x, alternative = "less")$p.value,
+           ks.test(x, y, alternative = "greater")$p.value)
[1] TRUE
> 
> proc.time()
   user  system elapsed 
  0.762   0.021   0.774