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A chi-square goodness-of-fit test for continuous distributions against a known alternative

Author

Listed:
  • Wolfgang Rolke

    (University of Puerto Rico)

  • Cristian Gutierrez Gongora

    (University of Puerto Rico)

Abstract

The chi square goodness-of-fit test is among the oldest known statistical tests, first proposed by Pearson in 1900 for the multinomial distribution. It has been in use in many fields ever since. However, various studies have shown that when applied to data from a continuous distribution it is generally inferior to other methods such as the Kolmogorov-Smirnov or Anderson-Darling tests. However, the performance, that is the power, of the chi square test depends crucially on the way the data is binned. In this paper we describe a method that automatically finds a binning that is very good against a specific alternative. We show that then the chi square test is generally competitive and sometimes even superior to other standard tests.

Suggested Citation

  • Wolfgang Rolke & Cristian Gutierrez Gongora, 2021. "A chi-square goodness-of-fit test for continuous distributions against a known alternative," Computational Statistics, Springer, vol. 36(3), pages 1885-1900, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-020-00997-x
    DOI: 10.1007/s00180-020-00997-x
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    References listed on IDEAS

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    1. Jin Zhang, 2002. "Powerful goodness‐of‐fit tests based on the likelihood ratio," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 281-294, May.
    2. J. Oosterhoff, 1985. "The Choice Of Cells In Chi–Square Tests," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 39(2), pages 115-128, June.
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