Description Usage Arguments Details Value Author(s) References See Also Examples
Compute the cdf of the Kolmogorov statistic for the two-sided test.
1 |
q |
vector of quantiles. |
n |
sample size. |
lower.tail |
logical; if TRUE (default) probabilities are P[X <= x], otherwise, P[X > x]. |
log.p |
logical; if TRUE, probabilities p are given as log(p). |
exact |
if TRUE use exact method, if FALSE use asymptotic aproximation, if NULL (default) use exact method for n<=100 and asymptotic for n>100. |
warn |
logical; if TRUE (default) and |
Avoid setting exact=TRUE for large values of n since the exact method can become very slow for such n.
This function is a wrapper for two undocumented low level R
functions which are used by ks.test
.
numerical vector of same length as q
containing the values of
the cdf of Kolmogorov's distribution.
Georgi N. Boshnakov; the essential computation is done by C functions by R Core Development Team in package stats (copied here since unexported).
See ks.test
and, in the R sources, ks.c
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | xi <- seq(0,1,length=100) # some x values
plot(xi,psi.pks(xi,4)) # cdf of D_4
lines(xi,psi.pks(xi,4))
lines(xi,psi.pks(xi,50),col="blue") # overlay the cdf of D_{50}
lines(xi,psi.pks(xi,100),col="red") # overlay the cdf of D_{100}
abline(h=0.95, col="brown")
# q : P(Dn < q) = 0.95 for selected values of n
psi.pks(0.6239385,4)
psi.pks(0.2940753,20)
psi.pks(0.1340279,100)
psi.pks(0.04294685,1000) # asymptotic approximation
n <- 8
plot(xi,psi.pks(xi,n,exact=FALSE)) # evaluate and plot asymptotic approx.
lines(xi,psi.pks(xi,n)) # overlay the exact cdf.
f1 <- function(x) psi.pks(x,10) # f1(x) computes cdf of D_10
f2 <- function(x) psi.pks(x,20) # f2(x) computes cdf of D_20
f3 <- function(x) psi.pks(x,100) # f3(x) computes cdf of D_100
curve(f1,0,1)
curve(f2,0,1,add=TRUE,col="blue")
curve(f3,0,1,add=TRUE,col="red")
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