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

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  • Horváth, Lajos

Abstract

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. repec:exl:29stat:v:20:y:2019:i:3:p:1-30 is not listed on IDEAS
    2. Baron, Michael & Rukhin, Andrew L., 2001. "Perpetuities and asymptotic change-point analysis," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 29-38, November.
    3. Verma Vivek & Nath Dilip C., 2019. "Characterization Of The Sum Of Binomial Random Variables Under Ranked Set Sampling," Statistics in Transition New Series, Statistics Poland, vol. 20(3), pages 1-29, September.
    4. Vivek Verma & Dilip C. Nath, 2019. "Characterization Of The Sum Of Binomial Random Variables Under Ranked Set Sampling," Statistics in Transition New Series, Polish Statistical Association, vol. 20(3), pages 1-29, September.

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