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## P(sup | F_n - F | > t) < 2 exp(-2nt^2)
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## P(sup | F_n - F | > t) < 2 exp(-2nt^2)
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##
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##
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## The 2 in front of exp() was derived by Massart. It is the best possible
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## The 2 in front of exp() was derived by Massart. It is the best possible
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## constant valid uniformly in t,n,F. For large n*t^2 this agrees with the
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## constant valid uniformly in t,n,F. For large n*t^2 this agrees with the
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## large-sample approximation to the Kolmogorov-Smirnov statistic.
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## large-sample approximation to the Kolmogorov-Smirnov statistic.
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##
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##
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superror <- function(rfoo,pfoo,sample.size,...) {
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superror <- function(rfoo,pfoo,sample.size,...) {
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    x <- rfoo(sample.size,...)
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    x <- rfoo(sample.size,...)
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    tx <- table(x)
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    tx <- table(signif(x, 12)) # such that xi will be sort(unique(x))
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    xi <- as.numeric(names(tx))
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    xi <- as.numeric(names(tx))
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    f <- pfoo(xi,...)
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    f <- pfoo(xi,...)
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    fhat <- cumsum(tx)/sample.size
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    fhat <- cumsum(tx)/sample.size
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    max(abs(fhat-f))
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    max(abs(fhat-f))
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}
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}