Browse > Article
http://dx.doi.org/10.3745/KIPSTA.2002.9A.2.267

An Effective Algorithm for the Noncentral Chi-Squared Distribution Function  

Gu, Son-Hee (Jeonju University)
Publication Information
The KIPS Transactions:PartA / v.9A, no.2, 2002 , pp. 267-270 More about this Journal
Abstract
The evaluation of the cumulative distribution function of the noncentral $\chi^2$ distribution is required in approximate determination of the power of the $\chi^2$ test. This article provides an algorithm for evaluating the noncentral $\chi^2$ distribution function in terms of a single "central" $\chi^2$ distribution function and compared various approximations.ximations.
Keywords
Algorithm; Noncentral Chi-Squared Distribution; Probabilities Values;
Citations & Related Records
연도 인용수 순위
  • Reference
1 T. J. Boardman and R. W. Kopitzke, 'Probability and table values for statistical distributions,' Proceedings of the Statistical Computing Section, American Statistical Association, pp.81-86, 1975
2 A. I. Abdel-Samad and S. K. Ashour, 'On the computation of non-central chi-square distribution function,' Communications in Statistics, Simulation and Computation, Vol.19(4), pp.1279-1291, 1990   DOI
3 R. A. Fisher, 'The general sampling distribution of the multiple correlation coefficient,' Proceedings of Royal Society of London, Vol.121A, pp.654-673, 1928
4 P. J. Bickel and K. A. Doksum, 'Mathematical Statistics : Basic ideas and selected topics,' San Francisco : Holden Day, 1977
5 W. C. Guenther, 'Another derivation of the non-central chi-square distribution,' Journal of the American Statistical Association, Vol.59, pp.957-960, 1964   DOI
6 N. L. Johnson, 'On an extention of the connection between Poisson and $x^2$ distributions,' Biometrika, Vol.46, pp.352-363, 1959
7 N. L. Johnson and S. Kotz, 'Continuous Univariate Distributions,' Boston: Houghton Mifflin, 1970
8 K. S. Miller and R. I. Bernstein and L. E. Blumenson, 'Generalized Rayleigh Process,' Quarterly of Applied Mathematics, Vol.16, pp.137-145, 1958   DOI
9 J. H. Park, 'Moments of the generalized Rayleigh distribution,' Quarterly of Applied Mathematics, Vol.19, pp.45-49, 1961   DOI
10 P. B. Patnaik, 'The non-central $x^2$ and F-distribution and their applications,' Biometrika, Vol.36, pp.303-332, 1949
11 H. O. Posten, 'Computer algorithm for the classical distribution functions,' in Proceedings for the First International Conference on the Teaching of Statistics, Sheffield, U.K. : University of Sheffield Printing Unit, pp.313-330, 1982
12 B. L. Shea, 'Chi-squared and incomplete Gamma integral,' Applied Statistics, Statistical Algorithms, Vol.37, pp.466-473, 1988   DOI   ScienceOn
13 H. R. Vaart, 'A note on the derivation of the non-central chi-square density function,' Statistica Neerlandica, Vol.21, pp.99-100, 1967   DOI