The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Test for Randomness of the Binary Random Sequence

이진확률수열의 무작위성 검정

  • Yeo, In-Kwon (Department of Statistics, Sookmyung Women's University)
  • Received : 2013.11.18
  • Accepted : 2014.01.09
  • Published : 2014.02.28
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Abstract

A test for randomness of the binary random sequence is proposed in this paper. The proposed test statistic is based on the mean length of runs distributed with truncated geometric distribution and asymptotically ${\chi}^2_2$-distributed when the size of the sequences is large. A small Monte Carlo simulation compared the size of the test with a significant level as well as evaluated the test power. We applied the proposed method to the sequence of yes or no numbers in Lotto 6/45 and concluded that the randomness of Lotto is retained.

이 논문에서는 이진확률수열의 무작위성을 검정하는 방법을 제안한다. 연의 길이는 절사된 기하분포를 따르는데 제안하고자 하는 검정통계량은 연의 평균길이를 기초로 하고 있으며 표본크기가 커지면 점근적으로 ${\chi}^2_2$-분포를 따른다. 검정크기와 검정력을 비교하기 위해 몬테칼로모의실험을 실시했다. 로또 6/45에서의 추첨여부에 대한 수열에 적용해 보았으며 로또는 무작위성을 만족하는 것으로 나타났다.

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References

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