Exact Computation of Pearson Statistics Distribution and Some Experimental Results

Authors

  • Marina V. Filina Steklov Mathematical Institute of RAS, Moscow, Russia
  • Andrew M. Zubkov Steklov Mathematical Institute of RAS, Moscow, Russia

DOI:

https://doi.org/10.17713/ajs.v37i1.294

Abstract

A Markov chain based algorithms for exact and approximate computation of Pearson statistics distribution for multinomial scheme are described. Results of computational experiments reveal some new properties of the difference between this distribution and corresponding chi-square distribution.

References

Good, I. J., Gover, T. N., and Mitchell, G. J. (1970). Exact distributions for Â2 and for likelihood-ratio statistic for the equiprobable multinomial distribution. Journal of the American Statistical Association, 65, 267-283.

Holzman, G. I., and Good, I. J. (1986). The Poisson and chi-squared approximation as compared with the true upper-tail probability of Pearson’s Â2 for equiprobable multinomials. Journal of Statistical Planning and Inference, 13, 283-295.

Selivanov, B. I. (2006). On the exact computation of decomposable statistics distributions for polynomial scheme (in russian). Diskretnaya matematika, 18, 85-94.

Zubkov, A. M. (1996). Recurrent formulae for distributions of functions of discrete random variables (in russian). Obozr. prikl. prom. matem., 3, 567-573.

Zubkov, A. M. (2002). Computational methods for distributions of sums of random variables (in russian). In Trudy po diskretnoi matematike (Vol. 5, p. 51-60). Moscow:

Fismatlit.

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Published

2016-04-03

How to Cite

Filina, M. V., & Zubkov, A. M. (2016). Exact Computation of Pearson Statistics Distribution and Some Experimental Results. Austrian Journal of Statistics, 37(1), 129–135. https://doi.org/10.17713/ajs.v37i1.294

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Articles