DOI QR코드

DOI QR Code

Goodness-of-fit test for the logistic distribution based on multiply type-II censored samples

  • Received : 2013.11.20
  • Accepted : 2013.12.09
  • Published : 2014.01.31

Abstract

In this paper, we derive the estimators of the location parameter and the scale parameter in a logistic distribution based on multiply type-II censored samples by the approximate maximum likelihood estimation method. We use four modified empirical distribution function (EDF) types test for the logistic distribution based on multiply type-II censored samples using proposed approximate maximum likelihood estimators. We also propose the modified normalized sample Lorenz curve plot for the logistic distribution based on multiply type-II censored samples. For each test, Monte Carlo techniques are used to generate the critical values. The powers of these tests are also investigated under several alternative distributions.

Keywords

References

  1. Balakrishnan, N. (1989). Approximate MLE of the scale parameter of the Rayleigh distribution with censoring. IEEE Transactions on Reliability, 38, 355-357. https://doi.org/10.1109/24.44181
  2. Balakrishnan, N., Kannan, N., Lin, C. T. andWu, S. J. S. (2004). Inference for the extreme value distribution under progressive type-II censoring. Journal of Statistical Computation & Simulation, 74, 25-45. https://doi.org/10.1080/0094965031000105881
  3. Balakrishnan, N. and Kateri, M. (2008). On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data. Statistics & Probability Letters, 78, 2971-2975. https://doi.org/10.1016/j.spl.2008.05.019
  4. Balakrishnan, N., Gupta, S. S., and Panchapakesan, S. (1995). Estimation of the mean and standard deviation of the logistic distribution based on multiply type-II censored samples. Statistics, 27, 127-142. https://doi.org/10.1080/02331889508802516
  5. Birnbaum, A. and Dudman, J. (1963). Logistic order statistics. The Annals of Mathematical Statistics, 34, 658-663. https://doi.org/10.1214/aoms/1177704178
  6. Choulakian, V. and Stephens, M. A. (2001). Goodness-of-fit tests for the generalized Pareto distribution. Technometrics, 43, 478-484. https://doi.org/10.1198/00401700152672573
  7. Cho, Y. S., Lee, J. Y. and Kang, S. B. (1999). A study on distribution based on the transformed Lorenz curve. The Korean Journal of Applied Statistics, 12, 153-163.
  8. Fei, H., Kong, F. and Tang, Y. (1995). Estimation for two-parameterWeibull distribution and extreme-value distribution under multiply type-II censoring. Communications in Statistics-Theory and Methods, 24, 2087-2104. https://doi.org/10.1080/03610929508831604
  9. Han, J. T. and Kang, S. B. (2008). Estimation for the double Rayleigh distribution based on multiply type-II censored samples. Communications of the Korean Statistical Society, 15, 367-378. https://doi.org/10.5351/CKSS.2008.15.3.367
  10. Kang, S. B., Cho, Y. S. and Han, J. T. (2008). Estimation for the half logistic distribution under progressive type-II censoring. Communications of the Korean Statistical Society, 15, 815-823. https://doi.org/10.5351/CKSS.2008.15.6.815
  11. Kang, S. B. and Cho, Y. S. (2001). A study on distribution based on the normalized sample Lorenz curve. The Korean Communications in Statistics, 8, 185-192.
  12. Kang, S. B. and Lee, S. K. (2006). Test for the exponential distribution based on multiply type-II censored samples. The Korean Communications in Statistics, 13, 537-550. https://doi.org/10.5351/CKSS.2006.13.3.537
  13. Kim, Y., Kang, S. B. and Seo, J. I. (2011a). Bayesian estimations on the exponentiated half triangle distribution under type-I hybrid censoring. Journal of Korean Data & Information Science Society, 22, 565-574.
  14. Kim, Y., Kang, S. B. and Seo, J. I. (2011b). Bayesian estimation in the generalized half logistic distribution under progressively type-II censoring. Journal of Korean Data & Information Science Society, 22, 977-987.
  15. Kus, C. and Kaya, M. F. (2006). Estimation of parameters of the loglogistic distribution based on progressive censoring using the EM algorithm. Hacettepe Journal of Mathematics and Statistics, 35, 203-211.
  16. Mathai, A. M. (2003). Order statistics from a logistic distribution and applications to survival and reliability analysis. IEEE Transaction on Reliability, 52, 200-206. https://doi.org/10.1109/TR.2003.813432
  17. Maswadah, M. (2003). Conditional confidence interval estimation for the inverse Weibull distribution based on censored generalized order statistics. Journal of Statistical Computation & Simulation, 12, 887-898.
  18. Nelson, W. (1982). Applied life data analysis, New York: Willy.
  19. Pettitt, A. N. and Stephens, M. A. (1976). Modified Cramer-von Mises statistics for censored data. Biometrika, 63, 291-298.
  20. Porter III, J. E., Coleman, J. W. and Moore, A. H. (1992). Modified KS, AD, and C-vM tests for the Pareto distribution with unknown location & scale parameters. IEEE Transactions on Reliability, 41, 112-117. https://doi.org/10.1109/24.126681
  21. Puig, P. and Stephens, M. A. (2000). Tests of fit for the Laplace distribution with applications. Technometrics, 42, 417-424. https://doi.org/10.1080/00401706.2000.10485715
  22. Shin, H. and Lee, K. (2012). Estimation in the exponential distribution under progressive type I interval censoring with semi-missing data. Journal of Korean Data & Information Science Society, 23, 1271-1277. https://doi.org/10.7465/jkdi.2012.23.6.1271

Cited by

  1. Estimation for the extreme value distribution under progressive Type-I interval censoring vol.25, pp.3, 2014, https://doi.org/10.7465/jkdi.2014.25.3.643
  2. Comprehensive comparison of normality tests: Empirical study using many different types of data vol.27, pp.5, 2016, https://doi.org/10.7465/jkdi.2016.27.5.1399
  3. 일반화된 로렌츠 곡선을 기반으로 한 Gumbel 분포의 적합도 검정 vol.28, pp.4, 2014, https://doi.org/10.7465/jkdi.2017.28.4.733