Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지

Parameter estimation for exponential distribution under progressive type I interval censoring

지수 분포를 따르는 점진 제1종 구간 중도절단표본에서 모수 추정

  • Received : 2010.08.08
  • Accepted : 2010.09.23
  • Published : 2010.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce a method of parameter estimation of progressive Type I interval censored sample and progressive type II censored sample. We propose a new parameter estimation method, that is converting the data which obtained by progressive type I interval censored, those data be used to estimate of the parameter in progressive type II censored sample. We used exponential distribution with unknown scale parameter, the maximum likelihood estimator of the parameter calculates from the two methods. A simulation is conducted to compare two kinds of methods, it is found that the proposed method obtains a better estimate than progressive Type I interval censoring method in terms of mean square error.

본 논문은 점진 제1종 구간 중도절단표본과 점진 제2종 중도절단표본에서 모수를 추정하는 방법을 소개하고, 점진 제2종 중도절단표본에서 모수를 추정하는 방법을 활용하고자 점진 제1종 구간 중도절단표본에서 얻은 자료를 변환하여 모수를 추정하는 새로운 방법을 제안하였다. 척도모수가 미지인 지수 분포를 따르는 점진 제1종 구간 중도절단표본을 이용하여 점진 제2종 중도절단표본의 최대우도추정량을 사용하여 모수를 추정하였고, 모의실험을 통하여 두 방법에서 구한 추정량을 비교한 결과 본 논문에서 새로 제시한 방법을 이용하여 구한 모수의 추정량이 평균제곱오차 측면에서 더 우수한 추정량임이 나타났다.

Keywords

References

  1. Aggarwala, R. (2001). Progressive interval censoring: Some mathematical results with applications to inference. Communications in Statistics-Theory and Methods, 30, 1921-1935. https://doi.org/10.1081/STA-100105705
  2. Amin, Z. H. (2008). A note on the parameter estimation for the lognormal distribution based on progressively Type I interval censored samples. Model Assisted Statistics Application, 3, 169-176.
  3. Ashour, S. K. and Afify, W. M. (2007). Statistical analysis exponentiated Weilbull Family under Type I progressive interval censoring with random removal. Journal of Applied Sciences Research, 3, 1851-1863.
  4. Balakrishnan, N. and Sandu, R. A. (1996). Best linear unbiased and maximum likelihood estimation for exponential distributions under general progressive TypeII censored sample. Sanky a : The Indian Journal of Statistics, 58, 1-9.
  5. Chen, D. G. and 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
  6. Cho, Y. S., Kang, S. B. and Han, J. T. (2009). The exponentiated extreme value distribution. Journal of the Korean Data & Information Science Society, 20, 719-731.
  7. Cohen, A. C. (1963). Progressively censoring censored samples in life testing. Technometrics, 5, 327-339. https://doi.org/10.2307/1266337
  8. Kalbfleisch, J. D. and Prentice, R. L. (2002). The statistical analysis of failure time data, Second edition, John Wiley, New York.
  9. Kang, S. B., Cho, Y. S. and Choi, S. Y. (2003). Tests for the exponential distribution based on Type-II censored samples. Journal of the Korean Data & Information Science Society, 14, 367-346.
  10. Kang, S. B., Cho, Y. S. and Han, J. T. (2005). Estimation for the double exponential distribution based on Type-II censored samples. Journal of the Korean Data & Information Science Society, 16, 115-126.
  11. Kang, S. B., Cho, Y. S. and Hwang, K. M. (1999). AMLE for the Rayleigh Distribution with Type-II censoring. Journal of the Korean Data & Information Science Society, 10, 405-413.
  12. Lawless, J. F. (2003). Statistical models and methods for lifetime data, John Wiley, New York.
  13. Lodon, D. (1988). Survival Models, Actex Publications, Connecticut.
  14. Ng, T. H. K. and Wang, Z. (2009). Statistical estimation for the parameters of Weibull distribution based on progressively Type-I interval censored sample. Journal of Statistical Computation and Simulation, 79, 145-159. https://doi.org/10.1080/00949650701648822
  15. Sun, J. (2006). The Statistical Analysis of Interval-censored Failure Time Data, Springer Verlag, New York.