# Algorithm 519: Three Algorithms for Computing Kolmogorov-Smirnov Probabilities with Arbitrary Boundaries and a Certification of Algorithm 487 S14

ALGORITHM 519 Three Algorithms for Computing KolmogorovSmirnov Probabilities With Arbitrary Boundaries and a Certification of Algorithm 487 [\$14J RALPH KALLMAN Ball State University Key Words and Phrases: Kolmogorov-Smirnov probabilities, sample distribution function, boundary crossing probability CR Categories: 5.5 Language: Fortran DESCRIPTION Introduction Let A ( y ) , B ( y ) be nondecreasing functions on [0, 1] where B(0) < 0 < A(0), B(1) < 1 < A(1). Let G~(y) be the sample distribution function for n independent random variables uniform on [0, 1]. We present three methods for computing P = Pr {B(y) < G~(y) < A ( y ) , y E [0, 1]}. The special case where A ( y ) = y ~ D, B ( y ) = y -- D has been treated by ACM Algorithm 487 [4]. Subroutine RAKK. A Generalization of Massey's Method Massey has given a recursion formula [3; 5, p. 341, eq. (11.7.9)] for computing P when A ( y ) = y -t- k/n, B ( y ) = y -- k/n. This can be generalized to arbitrary boundaries as follows. Let y(1, 3), y(2, 3) be the level points of B ( y ) , http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Mathematical Software (TOMS) Association for Computing Machinery

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