Geodesic
Exact and Limiting Probability Distributions of Some Smirnov Type Statistics
Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 93-103

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Let F(x) be the continuous distribution function of a random variable X and Fn(x) be the empirical distribution function determined by a random sample X1, ..., Xn taken on X. Using the method of Birnbaum and Tingey [1] we are going to derive the exact distributions of the random variables and and where the indicated sup' s are taken over all x' s such that -∞ < x < xb and xa ≤ x < + ∞ with F(xb) = b, F(xa) = a in the first two cases and over all x' s so that Fn(x) ≤ b and a ≤ Fn(x) in the last two cases. 
Csörgo, Miklós. Exact and Limiting Probability Distributions of Some Smirnov Type Statistics. Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 93-103. doi: 10.4153/CMB-1965-012-5
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     author = {Cs\"orgo, Mikl\'os},
     title = {Exact and {Limiting} {Probability} {Distributions} of {Some} {Smirnov} {Type} {Statistics}},
     journal = {Canadian mathematical bulletin},
     pages = {93--103},
     year = {1965},
     volume = {8},
     number = {1},
     doi = {10.4153/CMB-1965-012-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-012-5/}
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