An algorithm for generating chi random variables

ABSTRACT

An algorithm is presented for generating random variables from the chi family of distributions with degrees of freedom parameter LY 2 1. It is based on the ratio of uniforms method and can be used effectively for the gamma family.

REFERENCES

• 1: ANDERSON, T.W. Introduction to Multivariate Statistical Analysis. 2d ed. Wiley, New York, 1984.
• 2: BARTLETT, M.S. On the theory of statistical regression. In Proceedings of the Royal Society of Edinburgh, voI. 53 (1933}, 260-283.
• 3: BEST, D.J. Letter to the editor. Appl. Star. 27 (1978), 181.
• 4: R. C. H. Cheng , G. M. Feast, Gamma variate generators with increased shape parameter range, Communications of the ACM, v.23 n.7, p.389-395, July 1980 [doi>10.1145/358886.358893]
• 5: A. J. Kinderman , J. F. Monahan, Computer Generation of Random Variables Using the Ratio of Uniform Deviates, ACM Transactions on Mathematical Software (TOMS), v.3 n.3, p.257-260, Sept. 1977 [doi>10.1145/355744.355750]
• 6: KINDERMAN, A. J., AND MONAHAN, J.F. New methods for generating student's t and gamma variables. Computing 25 {1980), 369-377.
• 7: KI~UT,, D. E. The Art of Computer Programming, Vol. 2: Seminumerical Algorithms. Addison- Wesley, Reading, Mass., 1981.
• 8: P. A. W. LEWIS, A. S. GOODMAN, AND MILLER, J.M. A pseudorandom number generator for the system/360. IBM Syst. J. 8 (1969), 136-146.
• 9: Linus Schrage, A More Portable Fortran Random Number Generator, ACM Transactions on Mathematical Software (TOMS), v.5 n.2, p.132-138, June 1979 [doi>10.1145/355826.355828]

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Random number generation

Additional Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Efficiency

General Terms:
Algorithms, Measurement, Performance

Keywords:
chi distribution, gamma distribution, ratio of uniforms methods