  Functionals of Brownian bridge arise as limiting distributions in
nonparametric statistics. In this paper we will give a derivation of
distributions of extrema of the Brownian bridge based on excursion theory for
Brownian motion. Only the Poisson character of the excursion process will be
used. Particular cases of calculations include the distributions of the
Kolmogorov-Smirnov statistic, the Kuiper statistic, and the ratio of the
maximum positive ordinate to the minumum negative ordinate.
