Abstract
The algorithm calculates the exact cumulative distribution of the two-sided Kolmogorov-Smirnov statistic for samples with few observations. The general problem for which the formula is needed is to assess the probability that a particular sample comes from a proposed distribution. The problem arises specifically in data sampling and in discrete system simulation. Typically, some finite number of observations are available, and some underlying distribution is being considered as characterizing the source of the observations.
Supplemental Material
Available for Download
Von Neuman/Forsythe/Ahrens/Dieter/Brent: normal random numbers Gams: Von Neuman/Forsythe/Ahrens/Dieter/Brent
- 1 Ahrens, J.H., and Dieter, U. Computer methods for sampling from the exponential and normal distributions. Comm. ACM 15, 10 (Oct. 1972), 873-882. Google ScholarDigital Library
- 2 Ahrens, J.H., and Dieter, U. Pseudo-random Numbers (preliminary version). Preprint of book to be published by Springer, Part 2, Chs. 6-8.Google Scholar
- 3 Brent, R.P. Algorithms for Minimization Without Derivatives. Prentice-Hall, Englewood Cliffs, N.J., 1973, pp. 163-164.Google Scholar
- 4 Forsythe, G.E. Von Neumann's comparison method for random sampling from the normal and other distributions. Math. Comp. 26, 120 (Oct. 1972), 817-826.Google Scholar
- 5 Knuth, D.E. The Art of Computer Programming, Vol. 2. Addison-Wesley, Reading, Mass., 1969, pp. 26, 34, 464. Google ScholarDigital Library
- 6 Von Neumann, J. Various techniques used in connection with random digits. In Collected Works, Vol. 5, Pergamon Press, New York, 1963, pp. 768-770.Google Scholar
- 7 Bell, J.R. Algorithm 334, Normal random deviates. Comm. ACM 11, 7 (July 1968), 498. Google ScholarDigital Library
- 1 Bron, C. Algorithm 426, Merge Sort Algoriihm. Comm. ACM 15 (May 1972), 358. Google ScholarDigital Library
- 2 Bron, C. An "In Situ" Merge Sort Algorithm. Tech. Note CB 64, Technological University of Twente, Enschede. The Netherlands.Google Scholar
- 3 Martin, W.A. Sorting. Comp. Surv. 3 (1971), 147-174. Google ScholarDigital Library
- 1 Bellmore, M., and Nemhauser, G.L. The traveling salesman problem: A survey. Oper. Res. 16 (1968), 538-558.Google ScholarDigital Library
- 2 Berge, C. The Theory of Graphs and Its Applications. Wiley, New York, 1962.Google Scholar
- 3 Berge, C., and Ghouila-Houri, A. Programming, Games and Transportation Networks. Wiley, New York, 1965.Google Scholar
- 4 Boothroyd, J. Algorithms 22, 23, 24. Shortest path. Comp. J. 10 (1967), 306-308.Google Scholar
- 5 Lee, C.J. An algorithm for path connections andits applications. IEEE Trans. Elect. Comput. EC-IO (Sept. 1961), 346-365.Google ScholarCross Ref
- 6 Akers, S.B. A modification of Lee's path connection algorithm. IEEE Trans. Elect. Comput. (Feb. 1967), 97-98.Google ScholarCross Ref
Index Terms
- Algorithm 488: A Gaussian pseudo-random number generator
Recommendations
A fast normal random number generator
A method is presented for generating pseudorandom numbers with a normal distribution. The technique uses the ratio of uniform deviates method discovered by Kinderman and Monahan with an improved set of bounding curves. An optimized quadratic fit reduces ...
Fast pseudorandom generators for normal and exponential variates
Fast algorithms for generating pseudorandom numbers from the unit-normal and unit-exponential distributions are described. The methods are unusual in that they do not rely on a source of uniform random numbers, but generate the target distributions ...
Comments