Journal of the Korean Data Analysis Society

Korean Data Analysis Society (한국자료분석학회)
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Goodness of Fit Tests for the Exponential Distribution based on Multiply Progressive Censored Data

다중 점진적 중도절단에서 지수분포의 적합도 검정

  • Yun, Hyejeong (Division of Mathematics and Big Data Science, Daegu University) ;
  • Lee, Kyeongjun (Division of Mathematics and Big Data Science, Daegu University)
  • 윤혜정 (대구대학교 수리빅데이터학부 통계빅데이터전공) ;
  • 이경준 (대구대학교 수리빅데이터학부 통계빅데이터전공)
  • Received : 2018.11.20
  • Accepted : 2018.12.20
  • Published : 2018.12.31

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Abstract

Progressive censoring schemes have become quite popular in reliability study. Under progressive censored data, however, some units can be failed between two points of observation with exact times of failure of these units unobserved. For example, loss may arise in life-testing experiments when the failure times of some units were not observed due to mechanical or experimental difficulties. Therefore, multiply progressive censoring scheme was introduced. So, we derives a maximum likelihood estimator of the parameter of exponential distribution. And we introduced the goodness-of-fit test statistics using order statistic and Lorenz curve. We carried out Monte Carlo simulation to compare the proposed test statistics. In addition, real data set have been analysed. In Weibull and chi-squared distributions, the test statistics using Lorenz curve are more powerful than test statistics using order statistics.

최근에 중도절단 방법 중 점진적 중도절단과 관련한 연구가 활발히 이루어지고 있다. 하지만 점진적 중도절단 상황에서 관측되는 시점의 자료들 사이에는 관측원의 실수 혹은 관측 기계의 오류로 인하여 또 다른 중도절단이 발생할 수 있다. 따라서 이러한 기계적 오류 등을 고려하기 위하여 다중 점진적 중도절단이 새롭게 제안되었다. 따라서 본 논문에서는 다중 점진적 중도절단 상황에서 지수분포의 최대우도추정량을 계산하고 다중 점진적 중도절단 순서통계량을 이용한 적합도 검정 통계량과 로렌츠 곡선을 이용한 적합도 검정 통계량을 제안하였다. 몬테카를로 모의실험을 통하여 순서통계량을 이용한 적합도 검정 통계량과 로렌츠 곡선을 이용한 적합도 검정 통계량을 비교하고 더 우수한 적합도 검정 통계량을 확인하고, 실제 사례 자료를 활용하여 적합도 검정을 실시하였다. 그 결과 와이블분포와 카이제곱 분포의 경우 로렌츠 곡선을 이용한 방법이 더 우수한 결과가 나타났고, 로그 정규분포의 경우 순서통계량을 이용한 방법이 더 우수한 결과가 나타났다.

Keywords

Acknowledgement

Supported by : 대구대학교

References

  1. Asgharzadeh, A. (2009). Approximate MLE for the scaled generalized exponential distribution under progressive type II censoring, Journal of the Korean Statistical Society, 38, 223-229. https://doi.org/10.1016/j.jkss.2008.09.004
  2. Balakrishnan, N., Ng, H. K. T., Kannan, N. (2004). Goodness-of-fit tests based on spacings for progressively type-II censored data from a general location-scale distribution, IEEE Transaction on Reliability, 53, 349-356. https://doi.org/10.1109/TR.2004.833317
  3. Chen, D. G., Lio, Y. L. (2010). Parameter estimation for generalized exponential distribution under progressive type I interval censoring, Computational Statistics and Data Analysis, 54, 1581-1591. https://doi.org/10.1016/j.csda.2010.01.007
  4. Kang, S. B., Park, S. M. (2005). Estimation for the exponentiated exponential distribution based on multiply type II censored samples, The Korean Communications in Statistics, 12, 643-652.
  5. Kim, J., Lee, K. (2018). Estimation of the Weibull distribution under unified progressive hybrid censored data, Journal of the Korean Data Analysis Society, 20, 2189-2199.
  6. Lee, K., Cho, Y. (2017). Exact inference for competing risks model with generalized progressive hybrid censored exponential data, Journal of the Korean Data Analysis Society, 19, 565-575.
  7. Lee, K., Lee, J., Park, C. (2016). Estimation of the Weibull distribution based on generalized type I hybrid censored samples, Journal of the Korean Data Analysis Society, 18, 733-744.
  8. Lee, L., Park, C., Cho, Y. (2012). Estimation of the exponential distribution based on multiply progressive type II censored sample, Communications for Statistical Applications and Methods, 19, 697-704. https://doi.org/10.5351/CKSS.2012.19.5.697
  9. Lee, C., Park, C., Kim, J. (2016). A research for the maximum and minimum in some bivariate exponential distributions, Journal of the Korean Data Analysis Society, 18, 1217-1227.
  10. Nelson, W. (1982). Applied life data analysis, John Wiley and Sons, New York.
  11. Pakyari, R., Balakrishnan, N. (2013). Goodness-of-fit tests for progressively type-II censored data from location-scale distributions, Journal of Statistical Computation and Simulation, 83, 167-178. https://doi.org/10.1080/00949655.2011.625424
  12. Singh, U., Kumar, A. (2007). Bayesian estimation of the exponential parameter under a multiply type II censoring scheme, Austrian Journal of Statistics, 36, 227-238.
  13. Wang, B. (2008). Goodness-of-fit test for the exponential distribution based on progressively type-II censored sample, Journal of Statistical Computation and Simulation, 78, 125-132. https://doi.org/10.1080/10629360600944266
  14. Yun, N., Lee, K. (2018). Goodness of fit tests for progressively type II censored data from a Gumbel distribution, Journal of the Korean Data and Information Science Society, 29, 59-69. https://doi.org/10.7465/jkdi.2018.29.1.59