The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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The Shapiro-Wilk Type Test for Exponentiality Based on Progressively Type II Censored Data

전진 제 2종 중도절단자료에 대한 Shapiro-Wilk 형태의 지수검정

  • Received : 20100200
  • Accepted : 20100500
  • Published : 2010.06.30
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Abstract

This paper develops a goodness of fit test statistic to test if the progressively Type II censored sample comes from an exponential distribution with origin known. The test is based on normalizing spacings and Stephens (1978)' modified Shapiro and Wilk (1972) test for exponentiality. The modification is for the case where the origin is known. We applied the same modification to Kim (2001a)'s statistic, which is based on the ratio of two asymptotically efficient estimates of scale. The simulation results show that Kim (2001a)'s statistic has higher power than Stephens' modified Shapiro and Wilk statistic for almost all cases.

본 논문에서는 지수분포의 검정에 자주 쓰이는 Shapiro와 Wilk (1972) 통계량과 이의 단점을 보완한 Kim (2001a)의 통계량을 위치모수가 주어지고 척도모수가 미지인 지수분포에서의 전진 제 2종 중도절단자료에 적용하였다. 이를 위하여 각각의 통계량을 Stephens (1978)을 이용하여 위치모수가 주어진 경우의 검정통계량으로 수정하고, 자료를 정규화 간격(normalized spacings)을 이용하여 변환하는 방법을 사용하였다. 모의실험을 통하여 검정력을 비교한 결과 Shapiro-Wilk 통계량보다 Kim (2001a)의 통계량을 이용할 때 고려한 거의 모든 경우 더 우수한 검정력을 나타내었다.

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References

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