```
# NOT RUN {
require(graphics)
require(dgof)
set.seed(1)
x <- rnorm(50)
y <- runif(30)
# Do x and y come from the same distribution?
ks.test(x, y)
# Does x come from a shifted gamma distribution with shape 3 and rate 2?
ks.test(x+2, "pgamma", 3, 2) # two-sided, exact
ks.test(x+2, "pgamma", 3, 2, exact = FALSE)
ks.test(x+2, "pgamma", 3, 2, alternative = "gr")
# test if x is stochastically larger than x2
x2 <- rnorm(50, -1)
plot(ecdf(x), xlim=range(c(x, x2)))
plot(ecdf(x2), add=TRUE, lty="dashed")
t.test(x, x2, alternative="g")
wilcox.test(x, x2, alternative="g")
ks.test(x, x2, alternative="l")
#########################################################
# TBA, JWE new examples added for discrete distributions:
x3 <- sample(1:10, 25, replace=TRUE)
# Using ecdf() to specify a discrete distribution:
ks.test(x3, ecdf(1:10))
# Using step() to specify the same discrete distribution:
myfun <- stepfun(1:10, cumsum(c(0, rep(0.1, 10))))
ks.test(x3, myfun)
# The previous R ks.test() does not correctly calculate the
# test statistic for discrete distributions (gives warning):
# stats::ks.test(c(0, 1), ecdf(c(0, 1)))
# ks.test(c(0, 1), ecdf(c(0, 1)))
# Even when the correct test statistic is given, the
# previous R ks.test() gives conservative p-values:
stats::ks.test(rep(1, 3), ecdf(1:3))
ks.test(rep(1, 3), ecdf(1:3))
ks.test(rep(1, 3), ecdf(1:3), simulate=TRUE, B=10000)
# }
```

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