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The limit distributions of likelihood ratio and cumulative sum tests for a change in a binomial probability


  • Horváth, Lajos


We obtain limit theorems for likelihood ratio and cumulative sums tests. In the case of the likelihood ratio the centralising and normalising sequences go to infinity and the limit is the Gumbel (double exponential) distribution. The first and the last few observations determine the limit, which also explains why the likelihood ratio test is very powerful on the tails.

Suggested Citation

  • Horváth, Lajos, 1989. "The limit distributions of likelihood ratio and cumulative sum tests for a change in a binomial probability," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 148-159, October.
  • Handle: RePEc:eee:jmvana:v:31:y:1989:i:1:p:148-159

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    Cited by:

    1. Baron, Michael & Rukhin, Andrew L., 2001. "Perpetuities and asymptotic change-point analysis," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 29-38, November.


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