Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Comparison of Size and Power of Tests of Hypotheses on Parameters Based on Two Generalized Lindley Distributions

  • Okwuokenye, Macaulay (Biogen Idec) ;
  • Peace, Karl E. (Jiann-Ping Hsu College of Public Health, Georgia Southern University)
  • Received : 2014.12.30
  • Accepted : 2015.02.02
  • Published : 2015.05.31
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Abstract

This study compares two generalized Lindley distributions and assesses consistency between theoretical and analytical results. Data (complete and censored) assumed to follow the Lindley distribution are generated and analyzed using two generalized Lindley distributions, and maximum likelihood estimates of parameters from the generalized distributions are obtained. Size and power of tests of hypotheses on the parameters are assessed drawing on asymptotic properties of the maximum likelihood estimates. Results suggest that whereas size of some of the tests of hypotheses based on the considered generalized distributions are essentially ${\alpha}$-level, some are possibly not; power of tests of hypotheses on the Lindley distribution parameter from the two distributions differs.

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References

  1. Akaike, H. (1974). A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19, 716-723. https://doi.org/10.1109/TAC.1974.1100705
  2. Bender, R., Augustin, M. and Blettner, M. (2005). Generating survival times to simulate Cox's pro-portional hazards models, Statistics in Medicine, 24, 1713-1723. https://doi.org/10.1002/sim.2059
  3. Ghitany, M. E., Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application, Mathematics and Computers in Simulation, 78, 493-506. https://doi.org/10.1016/j.matcom.2007.06.007
  4. Lindley, D. V. (1958). Fiducial distributions and Bayes' theorem, Journal of the Royal Statistical Society Series B, 20, 102-107.
  5. Nadarajah, S. and Bakouch, H. S. and Tahmasbi, R. (2011). A generalized Lindley distribution, Sankhya B, 73, 331-359. https://doi.org/10.1007/s13571-011-0025-9
  6. Okwuokenye, M. (2012). Size and power of tests of hypotheses on parameters when modelling time-to-event data with the Lindley distribution (Doctoral dissertation), Georgia Southern University, Statesboro, GA.
  7. Peace, K. E. (1976). Maximum likelihood estimation and efficiency assessments of tests of hypotheses on survival parameters (Doctoral dissertation), Medical College of Virginia, Virginia Common-wealth University, Richmond, VA.
  8. Peace, K. E. and Flora, R. E. (1978). Size and power assessment of tests of hypotheses on survival parameters, Journal of the American Statistical Association, 73, 129-132. https://doi.org/10.1080/01621459.1978.10480015
  9. Qian, J., Li, J. and Chen, P. (2010). Generating survival data in the simulation studies of Cox model, In Proceedings of 2010 Third International Conference on Information and Computing (ICIC), Wuxi, China, 93-96.
  10. Rizopoulos, D. (2012). Joint Models for Longitudinal and Time-to-Event Data: With Applications in R, CRC Press, Boca Raton.
  11. Schwarz, G. (1978). Estimating the dimension of a model, Annals of Statistics, 6, 461-464. https://doi.org/10.1214/aos/1176344136
  12. Zakerzadeh, H. and Dolati, A. (2009). Generalized Lindley distribution, Journal of Mathematical Extension, 3, 13-25.

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